WO2008148250A1

WO2008148250A1 - Denoising method by signal reconstruction from partial spectrum data

Info

Publication number: WO2008148250A1
Application number: PCT/CN2007/001898
Authority: WO
Inventors: Jianhua Luo; Yuemin Zhu
Original assignee: Jianhua Luo; Yuemin Zhu
Priority date: 2007-06-08
Filing date: 2007-06-15
Publication date: 2008-12-11
Also published as: CN101067650A

Abstract

A denoising method by signal reconstruction from partial spectrum data includes the steps of: extracting various partial spectrum data from an intact signal spectrum space according to different frequency ranges, reconstructing a plurality of observing signals from the partial spectrum data above using complex singular spectrum analysis, and according to the plurality of reconstructed observing signals above, performing signal denoising by multiple observing signals averaging. With the denoising method by signal reconstruction from partial spectrum data, it has a combined advantage of denoising by multiple observing signals averaging and single observing signal denoising, scanning time is saved, image noise is effectively removed, and signal-to-noise ratio is improved.

Description

Signal Denoising Method Based on Partial Frequency Data Signal Reconstruction

The invention relates to the technical field of medical imaging detection, in particular to the field of noise removal of a magnetic resonance imaging fidelity signal, in particular to a signal denoising method based on partial frequency data signal reconstruction. Background technique

With the continuous development of modern medical technology, magnetic resonance imaging (MRI) technology has become an indispensable means in the field of medical imaging detection. Among them, the magnetic resonance signal space (raw data space) is called K space, which is Fourier. Transform space, K space sampled signal after Fourier inverse transform and then modulo, that is, to obtain nuclear magnetic resonance (MR) image.

The usual image signals contain various noises, and the noise can be divided into additive noise and multiplicative noise. The multiplicative noise is proportional to the size of the contaminated signal, and the additive noise is independent of the size of the contaminated signal. The observation signal with additive noise / (X) mathematical model can be expressed as:

f{x) = g(x) + ns(x), x = 0Χ..., Ν-1 ( 0 ) where and are represented as noise-free real signal sequences and noise signal sequences, respectively. In most cases, the sequence is a non-stationary signal, so the observed signal /(X) is also a non-stationary signal.

There are roughly three types of noise removal methods in the prior art:

The first category: multiple observation signal averaging method. The main idea is that the elements of the #-sequence can be considered as independent, uniformly distributed, zero-mean, stationary random variables. In this way, when the observed signal/(X) sequence acquired multiple times is superimposed and averaged, the random noise (x) will cancel each other weakly, thereby achieving the purpose of denoising. This method is currently recognized as a method of fidelity denoising and is widely used in medical equipment. But this method has the following drawbacks:

(1) It is difficult, sometimes even impossible, to repeatedly acquire observation signals from the same source. For example, when the source has random motion (such as heartbeat) and the source is a time-varying system (the ECG signal of arrhythmia patients) (please refer to the literature: He Wei, Xie Zhengxian, Studying Waveform Distortion of Electricardiac Signals Introduced By Signal -Averaged, CHINESE J MED PHYS Vol.16 No.l,Jan.l999,pp26-27 );

(2) Repeated collection of observation signals takes time and equipment to take up time, reducing equipment efficiency.

To this end, the following methods of denoising a single observed signal have been developed.

The second category: single observation signal neighborhood estimation method. The basic idea of this type of method is based on the assumption that /(X) can also be considered as approximately independent, identically distributed, zero-mean, stationary random variables in local small neighborhoods. This allows you to denoise / (X) with local spatial neighborhood estimates (such as mean, median, and fitted values). But in the vast majority of cases, Such methods often result in loss of signal detail and distortion. To this end, people have proposed a signal space i or method to improve signal fidelity (see literature: Charles, D.; Davies, ER, Distance-weighted median filters and their application to colour images, Visual Information Engineering, 2003. VIE 2003. International Conference on7-9 July 2003 Page(s): 117 - 120; Nai-Xiang Lian; Zagorodnov, V.; Yap-Peng Tan, Edge-preserving image denoising via optimal color space projection, Image Processing, IEEE Transactions on , Volume 15, Issue 9, Sept. 2006 Page(s): 2575-2587; Balster, EJ; Zheng, YF; Ewing, R丄., Combined spatial and temporal domain wavelet shrinkage algorithm for video denoising, Circuits and Systems for Video Technology, IEEE Transactions on Volume 16, Issue 2, Feb. 2006 Page(s): 220 - 230; Rosiles, JG; Smith, MJT, Image denoising using directional filter banks, Image Processing, 2000. Proceedings. 2000 International Conference on Volume 3, 10-13 Sept. 2000 Page(s): 292 - 295; and Han Liu; Yong Guo; Gang Zheng, Image Denoising Based on Least Sq Uares Support Vector Machines, Intelligent Control and Automation, 2006. WCICA 2006. The Sixth World Congress on, Volume 1, 21-23 June 2006 Page(s): 4180 - 4184 ). However, the drawback of this type of method is that the signal distortion problem of spatial denoising cannot be solved fundamentally.

The third category: single observation signal transform domain coefficient separation method. The basic assumptions of this type of method are: The noise pollution signal can be divided into signal transform domain coefficients and noise transform domain coefficients in the transform domain. The noise transform domain coefficients can be zeroed, and then the inverse transform method is used to reconstruct the noiseless signal. To the purpose of noise. Common methods are: Fourier transform, wavelet transform (see literature: Yunyi Yan; Baolong Guo; Wei Ni, Image Denoising: An Approach Based on Wavelet Neural Network and Improved Median Filtering, Intelligent Control and Automation, 2006. WCICA 2006. The Sixth World Congress on Volume 2, 21-23 June 2006 Page(s): 10063 - 10067; Hui Cheng; Qiuze Yu; Jinwen Tian; Jian Liu, Image denoising using wavelet and support vector regression. Image and Graphics, 2004. Proceedings. Third International Conference on 18-20 Dec. 2004 Page(s):43-46; Wink, AM; Roerdink, JBTM, Denoising functional MR images: a comparison of wavelet denoising and Gaussian smoothing, Medical Imaging, IEEE Transactions on Volume 23, Issue 3, March 2004 Page(s): 374 - 387; Nai-Xiang Lian; Zagorodnov, V.; Yap-Peng Tan, Color image denoising using wavelets and minimum cut analysis, Signal Processing Letters, IEEE Volume 12, Issue 11, Nov 2005 Page(s): 741-744; Chen, GY; Bui, TD; Krzyzak, A" Image denoising using neighbourin G wavelet coefficients, Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP Ό4). IEEE International Conference on Volume 2, 17-21 May 2004 Page(s): 917-202; Zhang, S.; Salari, E Image denoising using a neural network based non-linear filter in wavelet domain, Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP Ό5). IEEE International Conference on Volume 2, 18-23 March 2005 Page(s): 989 - 992 ) , Sparse Tranform (see literature: Li Shang; Deshuang Huang, Image denoising using non -negative sparse coding shrinkage algorithm, Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on, Volume 1, 20-25 June 2005 Page(s): 1017-1022; Guleryuz, OG, Nonlinear approximation based image recovery Using adaptive sparse reconstructions and iterated denoising-part I: theory, Image Processing, IEEE Transactions on, Volume 15, Issue 3, March 2006 Page(s):539-554; Elad, M.; Aharon, M., Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , Image Processing, IEEE Transactions on, Volume 15, Issue 12, Dec. 2006 Page(s): 3736 - 3745 ) , Hilbert-Huang Transform (see literature: Zhuo-Fu Liu; Zhen- Peng Liao; En-Fang Sang, Speech enhancement based on Hilbert-Huang transform, Machine Learning and Cybernet Ics, 2005. Proceedings of 2005 International Conference on , Volume 8, 18-21 Aug. 2005 Page(s): 4908-4912; Xiaojie Zou; Xueyao Li; Rubo Zhang, Speech Enhancement Based on Hilbert-Huang Transform Theory, Computer and Computational Sciences, 2006. IMSCCS Ό6. First International Multi-Symposiums on, Volume 1, 20-24 June 2006 Page(s): 208-213; Wu Wang; Xueyao Li; Rubo Zhang, Speech Detection Based on Hilbert-Huang Transform, Computer and Computational Sciences, 2006. IMSCCS '06. First International Multi- Symposiums on, Volume 1, 20-24 June 2006 Page(s): 290-293) and so on. In fact, so far, there is no single transform that can strictly distinguish the true signal and the noise transform's coefficients in the observed signal, which will inevitably lead to more or less signal loss. Summary of the invention

The object of the present invention is to overcome the above shortcomings in the prior art, and to provide a high frequency signal loss or signal distortion in the process of signal denoising, and an average denoising method for multiple observation signals and a single observation signal. The superiority of noise method, easy signal acquisition, effective image noise removal, accurate display of original magnetic resonance image, high efficiency and practicality, stable and reliable working performance, and wide application range of signal denoising based on partial frequency data signal reconstruction.

In order to achieve the above object, the signal denoising method based on partial frequency data reconstruction is as follows: The signal denoising method based on partial spectral data signal reconstruction includes the following steps:

(1) taking out various partial frequency data G(k) from different frequency bands from the complete signal spectrum space;

(2) reconstructing a plurality of observation signals by using a complex singular foreign language analysis method according to the above partial spectrum data;

(3) Denoising the signal by using the multiple observation signal averaging method based on the plurality of reconstructed observation signals. The reconstruction of the observed signal by the complex singularity analysis method in the signal denoising method based on partial frequency speech data signal reconstruction comprises the following steps:

(1) Obtaining an approximate signal of partial spectral data using the zero-padding method;

(2) performing model parameter estimation based on the approximate signal and the known partial spectral data G(k);

(3) Reconstruct the observation signal using the mathematical model of the observed signal and the complex singular spectrum analysis model based on the estimated model parameters.

The mathematical model of the observed signal in the signal denoising method based on partial frequency transmission data signal reconstruction is:

Where gc), x = 0, l, ..., N-1 is a complex digital signal, which is Q singular points on g(x), {H3⁄4(X), M3⁄4 ₂ (X),... , W _3⁄4 (X)} are Q singular functions that respectively assume singular points, which are complex singular values on the Q singular points, ... ^.

The complex singularity analysis model in the signal denoising method based on partial frequency data signal reconstruction is:

'where G(k = DFT(gc)) , W _bq {k) = DFT{w _hq {x)) , q = 0,l,...,Q , £» Τ(·) is discrete Leaf transform operator.

The model parameter estimation in the signal denoising method based on partial frequency and rich data signal reconstruction includes the following steps:

(1) Fill in the missing part of the part of the spectrum data, and obtain the Fourier spectrum data after the missing data is filled in according to the following formula.

G _z (k) = G(k)R _s _ _e (k);

Where is the Fourier spectrum data of the signal g(x),; c = 0, l, ..., N-1, = - N/2 - l, ..., N/2 - 1 ' where s To cut off the upper limit frequency, e is the cutoff lower limit frequency;

(2) Calculate d _z (x) according to the following formula:

0) = g _z O)—g _z O—i);

Where g^x r—' G :)), A = - N/2- l,...,N/2- 1, —〗 (·) denotes the inverse discrete Fourier transform operator;

(3) Sort the obtained moduli from large to small, and take the first L points as the pre-selected singular point set. { b _x , b ₂ ,...,b _L }, where L is the width of the rectangular function R _s —human k~), ie = _e - s , and the known spectrum is (4) constructing the singular spectrum according to the following formula equation:

( ⁵ ) Solving the singular spectral equation by the pseudo inverse matrix method to obtain a minimum error solution, and obtaining L complex singular values {aa ₂ ,..., a _L };

(6) Return α ₂ , . . . as the result of the model parameter estimation.

The reconstruction of the observed signal in the signal denoising method based on the partial frequency data reconstruction may be: based on the result of the model parameter estimation {α,, ,...,^}, reconstructing according to the following formula The observed signal g(x):

Or you can include the following steps:

(1) Based on the result of the model parameter estimation ^, ^, ...), the Fourier spectrum data Gik) is reconstructed according to the following formula:

(2) Obtaining the complex observation signal according to the following formula:

g(x) = DFT- ^l [G(k)], jc = 0, l".., N-1.

The signal denoising method using the multiple observation signal averaging method in the signal denoising method based on partial spectral data signal reconstruction includes the following steps:

(1) will be semi-spectral), . : =- N/2,...,-1,0,1, ...,ν and - ν,·..,— 1,0,1, .. ., ^/2-1 (0 <v<N/2) The reconstructed multiple observed signals / (X) sequences are superimposed, where /(X) = g(x) + ns(x), X = 0, 1, N - 1;

(2) Average the above signals as the final denoised signal, and the /(X) denoised signal is expressed as:

Among them, (χ) is a unit pulse function.

A signal denoising method based on partial frequency speech data signal reconstruction using the invention is used for actual magnetic resonance image denoising. The method steps are: extracting part of the spatial spectrum data from the complete Κ space, and reconstructing a plurality of observation signals by the complex singularity analysis method according to the partial κ spatial frequency data, and the observation signals and the original observation signals respectively have Different random noises and the same true noise-free signal are then used to remove noise using multiple observation signal averaging. Therefore, this method has the advantages of multiple observation signal average denoising method and single observation signal denoising method at the same time, and ingeniously avoids the problem that the multiple observation signal average denoising method is difficult to acquire the observation signal of the same real signal. At the same time, the signal distortion problem of the single observation signal denoising method is overcome, so that the image signal noise can be effectively removed and the signal-to-noise ratio is improved under the condition of ensuring high signal-to-noise ratio, high resolution and high precision of the image. It provides high-quality and reliable image information for medical MRI detection. At the same time, the method of the invention is efficient and practical, stable and reliable in work performance, and has wide application range, which brings great convenience to people's work and life, and also It has laid a solid theoretical and practical foundation for the further development of medical technology and the widespread application. DRAWINGS

FIG. 1 is a schematic diagram of a ^c + N/ 2) + 0 + W/ 2) function curve in a signal denoising method based on partial frequency chirp data signal reconstruction according to the present invention.

8

2 is a schematic diagram of comparison of noise 0) and its convolution + ζ(χ)] * ns(x) in a signal denoising method based on partial frequency data signal reconstruction according to the present invention.

3 is a schematic diagram showing the working principle of a signal denoising method based on partial frequency "resolution data signal reconstruction" according to the present invention. FIGS. 4a and 4b are respectively before and after the image denoising method using the present invention in an object simulated magnetic resonance imaging test. Image comparison diagram.

Figures 5a and 5b are schematic views showing the comparison of the enlarged images of the coordinates (x, y) in Figs. 4a and 4b in the range of 240 < x < 320, 360 < y < 440, respectively.

Fig. 6 is a schematic diagram showing the comparison of the gradation curves of the pixels of the 205th row of Figs. 4a and 4b.

Figures 7a and 7b are respectively a schematic diagram of image comparison before and after the image denoising method of the 88th sagittal plane in the actual human magnetic resonance imaging test using the present invention.

Figures 7c and 7d show the image denoising of the coronal surface of the crown in the actual human magnetic resonance imaging test. A schematic diagram of the comparison of images before and after the method.

Figures 7e and 7f are respectively a schematic diagram of image comparison before and after the image denoising method of the 88th cross section of the roll in the actual human magnetic resonance imaging test. detailed description

In order to more clearly understand the technical content of the present invention, the following embodiments are described in detail.

The invention collects complete k-space data from the actual magnetic resonance equipment, and then extracts some frequency data from the phase, and the phase encoding range is -N/2 ~ N/2 - 1 , where N is the phase encoding number of the complete K-space data. And using the complex singularity error analysis imaging method (CSSA method) of partial frequency and data to reconstruct the magnetic resonance image to achieve the purpose of denoising, so this method is called partial spectral data signal reconstruction denoising method (DSRPSD, Denoising) By Signal Reconstruction from Partial Spectrum Data ).

Before expounding the overall working process and working principle of the present invention, in order to clarify its technical meaning, the following definitions need to be given first:

Definition 1: Given a real or complex digital signal, the point where the difference is not zero is a singular point, the difference value at the singular point is a singular value, and the singular value can be a real number or a complex number. .

Definition 2: The real digital signal w(X^ = 0,l,...,N-l has a unique singularity, and the singular value of 1, is called a singular function, ie: .

If the complex digital signal g(x), x = 0, 1, ..., N-1 has Q singular points { , , ···, } , then the complex digital signal g(x) can be Q singular functions Complex linear functional representation of { w (X), w (x),..., w _1⁄2 (x) }: g(x)^a _q w _bq (x), x = 0,l,...,Nl ... (1) where, , ...^ is. A singular point, a complex singular value on .., }.

Using DFTW to represent the discrete Fourier transform operator, then the Fourier transform of (x) is recorded as:

G(k) = DFT(g(x)) ...... (2)

W _hq (k) = DFT(w _hq {x)) , b _q =0,l,...,Q (3) is represented by the Fourier transform of the formula (1), g(x) for: G{k)=^a _q W _bq {k), k = QX...,Nl ...... (4)

9=1 '

As long as any row of pixel values of the «resonant image is treated as a one-dimensional complex signal g( ), x = 0, 1, ..., N-1 , the image can be represented by a linear functional of the complex singular function.

The next step is an estimate of the model parameters. If only part of the spectral data is known, and the real image is not known, the singular points and singular values obtained directly by the difference method are impossible. However, the missing part of the partial frequency data can be zero-padded, and the inverse Fourier transform can be performed to obtain an approximate image. Thus, the approximate image can be used to estimate the singularity, and then the singular point and the complex singular value are determined by the method of solving the singular equations. '

Let the Fourier spectral data of the signal g( ), _x = 0, l, ..., N-1 be: G(k , k = -N/2-l,...,N/2-l > Then the missing data can be expressed as:

G ₂ (k) = G(k)R _s _ _e (k) (5) where . — _e (yt) is a rectangular function, defined as follows:

"1, 5· ≤ A: < e , , ,

R (k)^ ...... (6) s~ ^{eK }} [0, other

Where s is the cutoff upper limit frequency and e is the cutoff lower limit frequency.

The signal used to estimate the phase can be expressed as:

g _z {x) = DFT- G _z (k))

= DFT ~ G {k) R {k)) ... -. ()?

= DFT' ¹ (G( )) ® DF ¹ (R(k))

= g( )®r(x)

Which FT- ¹ (·) represents the discrete Fourier inverse transform operator, ® denotes convolution, jix) = DFTXky) is

According to mathematical theory, the deconvolution of equation (7) is generally not accurately calculated and cannot be obtained by deconvolution.

To do this, you need to look at the difference: Ilck_

= DFT- [li^]G _z (k))

= DFT- ¹ ([1 - e""]G(A:)i?(A;)) (9)

The above equation shows that the differential signal of g(x), x = 0, l, ..., N - 1 is convoluted by r(x), and its effect is as follows:

(1) The position of the singular point may drift;

(2) False positive singularities may appear in large numbers;

(3) The size of the singular value changes.

Let the width of the rectangle function R _s — _e (k) be L = e s, that is, the known spectrum is {G(^), G(ii: ₂ ),..., G(3⁄4)}, then The modules are arranged from large to small, taking the first L points as pre-selected singular point sets and constructing the singular spectral equation:

(10)

Define the matrix:

Then the solution is:

a = W ⁺ G ...... (ID where w ⁺ = c^w) - ¹ w ^r represents the pseudo inverse matrix of w, w ^r represents the conjugate transposed matrix of w, (w ^r w) ^-1 Represents the inverse matrix of w ^r w . Regardless of whether the above equation is over-determined or underdetermined, a pseudo-inverse matrix method can be used to obtain a minimum error solution, and L complex singular values { _αι , _β2 ,..., } are obtained.

At this time, if =0, 0 ' ≤ , Bay , 0 < ≤ is called a false positive singular point. Since fl, .=0, reconstructing the complex digital signal according to the above formula (1) or reconstructing the Fourier error data according to the above formula (4), the false positive singularity does not affect the reconstruction result.

Now, according to the above formula (0), the set of singular points is the corresponding singular value. {a _x , a ₂ ,...,a _Q } , the observed signal /0) and the real signal g(x) have the same set of singular points, and /0) corresponding to the singular point introduced by noise. The singular value becomes { +"^3⁄4), α ₂ +ra(b ₂ ), .·., i3⁄4 , then: β '

Fix) ^3⁄4 ∑ [« ₉ + ^ns (b _g ) , ( ^χ ) ...... (12)

Among them, it is related to the real signal spectrum (?(Α:) = Ζ^73⁄40)] and noise transmission

The relationship can be obtained by taking the (45) type of the Fourier transform

F(k) = G(k) + Ns(k) (14) The function is defined here:

, il, r =— N/2,—N/2 + l"..,v-1

U(k) = \ ...... (15)

[0, k = v, v + \,..., NI2-2, NI2—\

- Γθ, k =—Nll, —NI2L, v—

U k) = \ (16)

[1, ^ = v, v + l, ..., N/2-2, N/2-l ' where 0 < v < N/2.

Then /o) can be expressed as:

Substituting F(k) = G(k) + NsO) and « + ns(b _q )W _bq (k) into the first and second terms of the above equation, respectively, can be obtained:

/ (x) «- ¹ [just _{+ Ny (^ 1 + -?} 1 [9 +" 6 call).] · .. · (18)

?=1

The first term of the above formula is the reconstruction of the partial spectral data with zero-inverted Fourier transform, and the second term is the singular analytic reconstruction of the partial frequency-divided data.

Therefore, the singular spectrum analysis method using partial spectral data signal reconstruction can significantly denoise. The denoising method has the advantages of multiple observation signal average denoising method and single observation signal denoising method, and avoids the problem of signal acquisition of multiple observation signal average denoising method. The above conclusions can be proved as follows:

Q

Considering GW = 2 ( , then the above formula can be written as:

9=1 _ o _

^{f {x) «DFT - 1} [(G (k) + Ns (k)) U (k)] + DFT- 1 [G (k) U (k)] + DFT_ l [£ ns (b q) W _Bq (k)U(k)]

'

= g(x) +∑ns(b _q )w _b (x) * DFT-'iUik)] + ns(x) * DFT~ ^l [U(k)] where represents the convolution integral.

It can be proved that the original functions of υ(]) and ϋ(k) are:

N/2-v

DFT- [U(k)] = δ(χ) + ξ _χ (χ) (21) where:

(twenty two)

Q

Since 2s(b _q )w _bii (x) is a singular function weighted sum of random stationary noise, it is approximately 0, and its deviation is 7^, so the second term of (19) should be 0. Then there are: f(x) «g(x) + ns(x) * DFT~ ^l [U(k)] (23) Substituting (13) into the second term of the above formula:

N/2 + v

f (x) = g(x) + ns{x) * { ~ δ(χ) + ξ _χ (χ)} (24) If U(k, sum in: (10) is:

One, il, ^ = -N/2, -N/2 + l,...,-v-l

U(k) = < (26)

[0, k = -v, -v + l,..., ,l,...,N/2-l

The same can be obtained: g(x) + ns(x) * { ^N/ ^ ^+V S(x) + ξ ₂ (x)} (27) where

The sum of (17) and (20) is averaged:

,, , , .N/2 + v„,, ^(x) + ₂ (x).

g(x) + ns(x) * { δ(χ + ^3⁄41 ) ^{3⁄42 J} } (29)

N 2

, sin(2^ v/N) N/2 + v , ,

Since ~ ^- T -- ~~ - "~ , there are:

N " N

N/2 + vc, z'sin(2^xv/N) N/2 + v _/ ,

-S(x) ^ «—————— o(x) (30)

N N N

If you remember:

Then (29) can be written as:

N/2 + v

f (x) « g(x) + ns(x) * { ~ —S(x) + ζ(χ)} (32)

(1) If v = N/2, ζ(χ)≡0, then / (x) = gO) + raO;), returning to formula (0), there is no denoising ability;

(2) If ν = 0., ζ(χ)≡0:

f(x)^g(x) + 0.5ns(x) ...... (33) However, it is possible that line streaks appear in the image at this time, which deteriorates the image quality.

(3) To suppress linear stripes, increase the V value. For example v = N/8, Fix) « g(x) + i^S(x) + ζ(χ)] * ns(x) (34)

8

Figure 1 is a plot of ^^(x + N/2) + ( ; + N/2) functions for N = 256 and v = N/8. Figure 2 is a comparison of the noise ra(x) and its convolution + ζ 0)] * ns{x). According to the periodic convolution property, the standard deviation relationship of 3⁄4S(X) and is:

STD(ns(x))≤ -STD(ns{x)) ...... (36)

8

Where STD represents the standard deviation operator. As shown in Figure 2, the fis(x) ratio is greatly reduced. '

Referring to FIG. 3, the signal denoising method based on partial frequency speech data signal reconstruction of the present invention comprises the following steps: (1) extracting various partial spectrum data G according to different frequency bands from a complete signal spectrum space ( k);

(2) reconstructing a plurality of observation signals by using the complex singularity analysis method according to the partial frequency data described above; the reconstruction processing includes the following steps:

(a) obtaining an approximation signal of the partial spectral data G(k) using the zero-padding method;

(b) estimating the model parameters according to the approximate signal and the known partial spectral data G(k); the mathematical model of the corresponding complex observed signal is: x = , l, ..., N-l;

Where g(x), x = 0, l, ..., N-1 is a complex digital signal, (^^,...,^^ is ^) Q singular points, {>3⁄40), ^ ₂ 0),...,^ 0)} are Q singular functions with singular points respectively, , a, a ₂ ,..., a _Q is the Q singular points} Complex singular value.

The corresponding complex singular spectrum analysis model is:

G( =|]"„), A; = 0,1"."N-1; where G(k) ₌ DFT(g(x)), W _bq (k) = DFT(w _h (x) ), q = 0,l,...,Q, FT *) is discrete Leaf transform operator

The model parameter estimation includes the following steps:

(i) Zero-padding the missing portion of the partial spectral data G(k), and obtaining the Fourier spectral data G _z (k) after the missing data is zero-padded according to the following formula:

G _z (k) = G(k)R _s _ _e (k);

Where G(J~) is the signal of g(x), X = 0, 1, ..·, N - 1 , and K = -N/2-l,...,N/2 -l^

R (Α = < , ^{5≤ <e} is a rectangular function, where s is the cutoff upper limit frequency and e is the cutoff lower limit frequency; ί ^_ ) [0, other

( ϋ ) Calculate d ₂ (JC) according to the following formula:

Representing a discrete Fourier inverse transform operator;

(iii) ordering the obtained d _s (x) modulo from large to small, and taking the first L points as pre-selected singular point sets

}, where L is the width of the rectangular function i^ _e (3⁄4;), ie =e- ^ and the known spectrum is

(iv) Construct a singular spectral equation according to the following formula:

w _bl i ) w _bi {k _L ) ... wk \ ^a iJ

(v) Solving the singular spectral equation by pseudo-inverse matrix method, obtaining a minimum error solution, and obtaining L complex singular values

(vi) return { _Ωι , a ₂ ".., a _L } as the result of the model parameter estimation;

(c) reconstructing the complex observation signal using the singular function mathematical model of the observed signal and the complex singular spectrum analysis model according to the results of the model parameter estimation; the reconstruction of the complex observation signal can be:

Based on the results of the model parameter estimation, the complex observation signal go) is reconstructed according to the following formula:

s.

g(x)=^a _(l w _bq (x), χ = 0Χ..., Ν-1;

g=\

Or you can include the following steps:

(i) reconstructing the described Fourier spectrum according to the results of the model parameter estimation according to the following formula Data

(ii) obtaining the complex observation signal g(JC) according to the following formula:

g{x) = DFr G(k)], JC = 0,1,...,N-1;

(3) performing image signal removal noise processing using the multiple observation signal averaging method according to the plurality of observation signals described above, the noise removal processing being:

The reconstructed plurality of observed signals g(x) sequences are superimposed and averaged as the final magnetic resonance complex image signal.

In actual use, the basic idea of the invention is that any row of pixel values of the «I resonance image is regarded as a one-dimensional complex signal gO), :c = 0,1,...,N-1, the image can be used The linear functional representation of the singular function, the partial frequency data signal reconstruction method can be applied. For magnetic resonance K-space data, it can be reconstructed from _x , two directions, and then each is averaged to achieve the denoising effect. At the same time, the reciprocal values from the two directions can also suppress the adverse effects of the linear stripes.

In the following experiment, V in equation (32) is a key important parameter. If V is too large (V = N/2), there is no denoising ability. If V is too small (V =0), stripe artifacts will be introduced. For a large number of tests, it is appropriate to select V = N/8. V = N / 8o is used in the following experiments - the test indicators in the experiment are as follows:

(1) Comparison of the Profile Line before and after image enhancement. A line graph is a gray scale with a position change curve on a certain row or column of an image, which can easily make a difference in gray scale between images.

(2) Image before and after image enhancement.

(3) Comparison of signal to noise ratio.

Experiment 1: Actual water model magnetic resonance imaging. Referring to FIG. 4 to FIG. 6, the real face data is scanned by the FLASH method, and the image size is 512x512, Te=0.172ms, Tr=400ms, and the average number is 2. The image is a model for testing the imaging resolution. The characteristics of this image are:

(1) There is a raster in the image, which can be used to test the image spatial resolution of the algorithm;

(2) The image phase changes more sharply.

4a and 4b are respectively a schematic diagram of comparison before and after image enhancement of the magnetic resonance model. It can be seen that Figure 4b has substantially removed the noise and is clearer than Figure 4a. The signal-to-noise ratios of Figures 4a and 4b are 24.05 and 36.54, respectively. Figure 5a and Figure 5b is a raster enlarged image of coordinates (x, y) in Figs. 4a and 4b, respectively, in the range of 240 < x < 320, 360 < y < 440. From the comparison of the fence images in Fig. 5a and Fig. 5b, it is found that the partial frequency data signal reconstruction denoising method can not only make the spatial resolution not weaken, but slightly increase. Figure 6 is a comparison of the line drawing of line 205 of Figures 4a and 4b. The two curves in Fig. 6 are line graphs of the 205th row of pixels of the images of Figs. 4a and 4b, respectively. It can be seen from the figure that the curve 2 corresponding to FIG. 4b is flat and smooth at the noise and denoised with respect to the curve 1 corresponding to FIG. 4a, and remains intact at the grating. The method of the present invention is described as having the function of denoising to protect image details.

Real 2: Actual magnetic resonance imaging. Referring again to Figures 7a to 7f, where Tl MPR3D SAG lmm, field of view height = 350 mm, width = 263 mm, length = 350 mm, , TR = 1.97 s, ΤΕ = 4.69 ms, image resolution 176 x 256 x 256. Before and after image denoising, the signal-to-noise ratio of the entire volume image is enhanced by about 1.6 times. Figures 7a and 7b are two images before and after denoising of the 88th sagittal plane in the roll, and Figures 7c and 7d are respectively two images before and after denoising of the 88th coronal surface in the roll, respectively. Figures 7e and 7f are volumes respectively. Two images of the 88th piece of the cross section. Figures 7a, 7c and 7e are both unnoised images, and Figures 7b, 7d and 7f are both denoised images. As is apparent from the above, the image effects of Figs. 7b, 7d, and 7f appear more clear than those of Figs. 7a, 7c, and 7e, indicating that the method of the present invention has a good denoising effect on images of various structures.

Experiment 3: Repeat the method for denoising analysis. The actual water model magnetic resonance image and the K data of the actual magnetic resonance image are repeatedly used to denoise the method of the present invention, and the signal-to-noise ratio after each denoising is as shown in Table 1 below. However, there are errors in the process of reconstructing the image. Repeated use of partial spectral data signal reconstruction denoising method to accumulate this error, so excessive use of this method also has side effects. The general use frequency should not exceed 2.

Table 1. Relationship between number of substitutions and signal to noise ratio

The signal denoising method based on the partial frequency data signal reconstruction is adopted, because it collects complete K-space data from the actual magnetic resonance equipment, and then takes part of the K-space frequency data, and passes the part K-space spectrum data according to the part. The complex singularity analysis method (CSSA method) reconstructs multiple observation signals, and these observation signals have different random noise and the same true noiseless signal from the original observation signals, and then use the multiple observation signal averaging method to remove noise. At the same time, it has the advantages of multiple observation signal average denoising method and single observation signal denoising method, and skillfully avoids the problem that the multiple observation signal average denoising method is difficult to collect the same real signal observation signal, and overcomes the problem. The signal distortion problem of single observation signal denoising method, which saves the scanning time under the condition of high signal-to-noise ratio, high resolution and high precision of the image, and can effectively remove image noise for medical nuclear magnetic resonance Imaging inspection provides high quality Reliable image information; At the same time, the method of the invention is efficient and practical, the work performance is stable and reliable, and the scope of application is wide, which brings great convenience to people's work and life, and also further develops medical technology and technology. Wide-ranging universal application has laid a solid theoretical and practical foundation.

In this specification, the invention has been described with reference to specific embodiments thereof. However, it is apparent that various modifications and changes can be made without departing from the spirit and scope of the invention. Accordingly, the specification and drawings are to be regarded as illustrative rather .

Claims

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A signal denoising method based on partial frequency data signal reconstruction, characterized in that the method comprises the following steps:

(1) from the full signal spectrum space, taken at different portions of the frequency bands of various data · ΐ P ^G ();

(2) reconstructing a plurality of observation signals by using a complex singular spectrum analysis method according to the above partial frequency data;

(3) Denoising the signal by using the multiple observation signal averaging method based on the plurality of reconstructed observation signals.

2. The signal denoising method based on partial frequency data signal reconstruction according to claim 2, wherein the reconstructing the observation signal by using the complex singularity analysis method comprises the following steps:

(1) obtaining an approximation signal of partial spectral data ^G W using a zero-padding method;

(2) performing model parameter estimation based on the approximate signal and the known partial spectrum data;

(3) Reconstruct the observation signal using the mathematical model of the observed signal and the complex singularity analysis model based on the estimated model parameters.

3. The signal denoising method based on partial frequency speech data reconstruction according to claim 2, wherein the mathematical model of the observed signal is:

Q

Q 1 is singular on the complex digital signals,} is ^{^{0) - gO) = Σ fl}} w (x), x =, l, ..., Nl wherein, 0) '= 0, 1,'"^ point, {^ »)" · "} ^^ respectively to,, ..., _Q} as a singular point singularity," ₁₃ _"2, ...," ₂ is a singular point of the {Q, , complex singular value on "', }.

The signal denoising method based on partial spectral data signal reconstruction according to claim 3, wherein the complex singular spectrum analysis model is:

G{k)=^a _q W _b {k), k = 0,\,...,Nl where GW = 7 g(x)), W _bq (k) = DFT{w _bq (x)) ^ _q = 0,l,...,Q ^ 7» is a discrete Fourier transform operator.

The signal denoising method based on the partial frequency data signal reconstruction according to claim 4, wherein the performing model parameter estimation comprises the following steps: (1) Zero-padding the missing part of the spectrum data, and obtaining the Fourier spectrum data after the missing data is zero according to the following formula:

G ₂ (k) = G{k)R _s _ _e (k).

Where ^G is the signal g ( ^ = 0, l, ..., ^ - 1 of the Fourier spectrum data = - N/2 - l".., N/2 - 1 , "1, s ≤ k <e

, 兵匕 is a rectangular function, where s is the cutoff upper limit frequency and e is the cutoff lower limit frequency;

(2) Calculated according to the following formula

d _z (x = g _z (. ^x )-gz( ^x - ^l ) _;

among them,

Representing a discrete Fourier inverse transform operator;

(3) Sort the obtained ^W 's modules from large to small, and take the first L points as pre-selected singular points.

{ ^bb 2'- } , where L is the width of the rectangular function ^R s ^{-human k} , ie = e- s , and the known spectrum is {G(k _x ), G(k ₂ ),...,G (k _L )} .

(4) Construct a singular spectral equation according to the following formula:

(5) Solving the singular spectral equation by pseudo-inverse matrix method, and obtaining a minimum error solution, and obtaining L complex singular values {aa ₂ ,..., a _L } .

( ₆ ) Return { A ' , · · ·, } as the result of the model parameter estimation.

6. The signal denoising method based on partial frequency and frequency data signal reconstruction according to claim 5, wherein the reconstructing the observed signal is: based on a result of model parameter estimation, ... , ^} , reconstructing the complex observation signal g ^W according to the following formula:

0

g(x)= w _A (x), x = 0,l,...,Nl

Oh ;

Or include the following steps: (1) Reconstructing the Fourier spectrum data according to the following formula based on the result of the model parameter estimation { ^a i' ^fl2 '"', ^}

;

(2) Obtaining the complex observation signal g ( : according to the following formula:

g(x) = DFT- ¹ [G(k)], x = 0,l,...,Nl.

The signal denoising method based on partial frequency data signal reconstruction according to claim 6, wherein the signal removal noise processing using the multiple observation signal averaging method comprises the following steps:

(1) will be semi-spectral ( ), =- N/2"..,-l,0,l"."v and -V".·, - l,0,l"."N/2- l ₍ o < v < N / 2) The reconstructed plurality of observed signal sequences are superimposed, where 0) = g( ^x ) + ^ra ( ^x ), x = 0, 1, ..., N _ 1;

(2) Average the above signals as the final denoised signal. The denoised signal is expressed as: f(x) « g(x) + ns{x) * {^^-S(x) + ζ(χ)}

0, χ = 0

Sin(2^xv/N) , πχ, _η

, ctg(- ), χ≠0

Where N Ν is a unit pulse function.