CN114528871B - Noise reduction method using fractional wavelet decomposition and reconstruction technology - Google Patents
Noise reduction method using fractional wavelet decomposition and reconstruction technology Download PDFInfo
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Abstract
The invention provides a noise reduction method by utilizing fractional wavelet decomposition and reconstruction technology, which aims at the defect of signal noise reduction processing by adopting wavelet decomposition reconstruction technology, changes the fixed forms of a wavelet decomposition high/low pass filter and a reconstruction high/low pass filter according to fractional calculus theory thought, changes the original limited threshold algorithm form, ensures that the filter form and the threshold algorithm form can be flexibly adjusted according to the actual condition of a processed signal, and finally achieves the effect of improving noise reduction. The invention has the advantages that the prior wavelet decomposition and reconstruction technology and threshold filtering technology have more and better technical effects, the technical problems of single and fixed wavelet decomposition and reconstruction filter form and limited threshold algorithm form are solved, and obvious progress is made in improving the visual effect of image signals and noise reduction precision.
Description
Technical Field
The invention relates to the field of signal processing, in particular to a signal noise reduction processing method.
Background
At present, the process of performing signal noise reduction processing by utilizing wavelet decomposition and reconstruction technology and combining a threshold value is as follows:
x=x+40X randn (size (X)) is a noise-containing signal, where X is the Matlab system self-contained original image woman and 40X randn (size (X)) is an externally applied white noise signal. And decomposing the noise-containing signal by using a wavelet decomposition technology in a first layer, a second layer and a third layer respectively, and filtering the high-frequency component by adopting a threshold value, wherein the adopted wavelet function name is 'sym5', and then performing wavelet reconstruction to finish the noise reduction treatment of the noise-containing signal. The processing result is divided into two parts: one part is an image simulation effect diagram, the other part is the maximum error value of the image after noise reduction compared with the original image, and the results are shown in (a), (b) and (c) in fig. 3, 4 and 5 and table 1 respectively.
TABLE 1 maximum error value table for relative to original image after wavelet decomposition and reconstruction
| Sequence number | Number of wavelet decomposition layers | Threshold vector | Maximum error value |
| 1 | 1 | [34 50] | 146.36 |
| 2 | 2 | [87 87] | 146.23 |
| 3 | 3 | [97 97] | 147.18 |
Through analysis, the noise reduction is carried out by the existing wavelet decomposition and reconstruction technology, and the effect can only reach the above results. In order to improve the noise reduction processing effect, many threshold modification technologies, such as soft threshold and hard threshold technologies, are also presented. However, these techniques have limited improvement in noise reduction.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a noise reduction method by utilizing fractional wavelet decomposition and reconstruction technology. Aiming at the defect of signal noise reduction processing by adopting a wavelet decomposition reconstruction technology, the invention changes the fixed forms of a wavelet decomposition high/low pass filter and a reconstruction high/low pass filter according to the fractional calculus theory idea, changes the original limited threshold algorithm form, ensures that the filter form and the threshold algorithm form can be flexibly adjusted according to the actual condition of the processed signal, and finally achieves the effect of improving noise reduction.
The technical scheme adopted by the invention for solving the technical problems comprises the following specific steps:
Step 1: invoking noisy signals
Reading the noise-containing signal under Matlab or other platforms, namely completing calling the noise-containing signal;
step 2: performing fractional wavelet decomposition on the noise-containing signal to generate a new wavelet coefficient matrix;
Firstly, fractional calculus changes are carried out on wavelet decomposition high-pass filter coefficients and low-pass filter coefficients, so that the filter form changes along with the change of the integral times of fractional calculus; secondly, the fractional wavelet decomposition high-pass filter coefficient and the low-pass filter after fractional calculus change are applied to the generation process of four sub-bands; the method comprises the following specific steps:
(a) LL subband;
after the boundary of the two-dimensional noise-containing signal in the horizontal direction is prolonged, carrying out convolution processing by using a fractional wavelet decomposition low-pass filter, carrying out downsampling on each row vector, after the boundary of the two-dimensional noise-containing signal in the vertical direction is prolonged, carrying out convolution processing by using the fractional wavelet decomposition low-pass filter, and carrying out downsampling on each column vector to obtain an approximate wavelet coefficient matrix FCA of the image signal;
(b) HL sub-band
After the two-dimensional noise-containing signal is prolonged at the boundary in the horizontal direction, performing convolution processing by using a fractional wavelet decomposition low-pass filter, performing downsampling on each row vector, and after the two-dimensional noise-containing signal is prolonged at the boundary in the vertical direction, performing convolution processing by using a fractional wavelet decomposition high-pass filter, performing downsampling on each column vector, and obtaining a wavelet coefficient matrix FCH of the image signal;
(c) LH sub-band
The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition low-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCV of the image signal;
(d) HH sub-band
The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCD of the image signal;
step 3: threshold processing is carried out on the high-frequency coefficients in three directions;
Thresholding the high frequency coefficients in the horizontal, diagonal, and vertical directions to generate new coefficient matrices FNA, FNH, FNV and FND;
Step 4: reconstructing signal wavelets;
Firstly, carrying out fractional calculus change on wavelet reconstruction high/low pass filter coefficients, changing the original fixed form, and enabling the filter form to change along with the change of the integral times of fractional calculus; secondly, a wavelet reconstruction high/low pass filter changed by a plurality of times of calculus is applied to the generation process of four reconstruction coefficient matrixes; the method comprises the following steps:
(a) Approximating the reconstruction coefficient matrix FCA';
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNA of the image signal, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete column vector interception, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction low-pass filter to complete row vector interception, so that an approximate reconstruction coefficient matrix FCA' of the image signal is obtained;
(b) Reconstructing coefficient matrix FCH'
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNH of the image signal, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCH' of the image signal is obtained;
(c) Reconstructing coefficient matrix FCV'
And after up-sampling and boundary extension are carried out on each column vector of the coefficient matrix FNV of the image signal, convoluting with a fractional wavelet reconstruction low-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convoluting with a fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so as to obtain a reconstruction coefficient matrix FCV' of the image signal.
(D) Reconstructing coefficient matrix FCD'
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FND of the image signal, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCD' of the image signal is obtained;
step5: recovering after noise reduction of the signal;
Adding the approximate reconstruction coefficient matrix obtained in the step 4 to the reconstruction coefficient matrix to obtain a noise-reduced signal, namely: FX '=fca' +fch '+fcv' +fcd ', FX' is the resulting noise reduced signal.
The soft threshold algorithm is adopted to make fractional calculus change, so that the existing soft threshold algorithm is continuously changed along with the change of the integral times of fractional calculus, the processed signal is better adapted, and a better threshold filtering effect is achieved; the adopted soft threshold algorithm performs fractional calculus change; according to actual needs, carrying out wavelet first-layer wavelet decomposition, second-layer wavelet decomposition and three-layer wavelet decomposition on the noise-containing signal respectively, wherein the scale vector setting is determined by the number of wavelet decomposition layers, and the threshold vector is set according to actual needs; the coefficient matrices FCA, FCH, FCV and FCD of the LL, HL, LH, and HH subbands are respectively subjected to soft threshold filtering in the horizontal, diagonal, and vertical directions, to correspondingly generate new coefficient matrices FNA, FNH, FNV and FND.
The invention has the beneficial effects that the prior wavelet decomposition and reconstruction technology and threshold filtering technology have more and better technical effects due to the adoption of the fractional calculus change technical means of the wavelet decomposition and reconstruction high/low pass filter and the fractional calculus change technical means of the soft threshold algorithm, the technical problems of single fixed form and limited threshold algorithm form of the wavelet decomposition and reconstruction filter are solved, and obvious progress is made in improving the visual effect of image signals and noise reduction precision.
Drawings
Fig. 1 is a flowchart of a noise reduction process of a conventional wavelet decomposition and reconstruction technique.
Fig. 2 is a flow chart of a noise reduction process for the fractional wavelet decomposition and reconstruction technique.
FIG. 3 is a graph showing the comparison of the effects of a layer of wavelet decomposition and reconstructed images applied by an example of the new invention. Wherein fig. 3 (a) is an original image woman, fig. 3 (b) is a noise-containing signal, fig. 3 (c) is an effect diagram of noise reduction on a noise-containing image by using a conventional wavelet decomposition and reconstruction technique, and fig. 3 (d) is an effect diagram of noise reduction on a noise-containing image by using a fractional wavelet decomposition and reconstruction technique.
Fig. 4 is a comparison graph of the effects of two-layer wavelet decomposition and reconstruction images applied to the new embodiment of the invention, in which fig. 4 (a) is an original image woman, fig. 4 (b) is a noise-containing signal, fig. 4 (c) is a graph of the effects of the conventional wavelet decomposition and reconstruction technique on noise-containing images, and fig. 4 (d) is a graph of the effects of the fractional wavelet decomposition and reconstruction technique on noise-containing images.
Fig. 5 is a graph comparing the effects of three-layer wavelet decomposition and reconstruction images applied by the novel invention example. Wherein fig. 5 (a) is an original image woman, fig. 5 (b) is a noise-containing signal, fig. 5 (c) is an effect diagram of noise reduction on a noise-containing image by using a conventional wavelet decomposition and reconstruction technique, and fig. 5 (d) is an effect diagram of noise reduction on a noise-containing image by using a fractional wavelet decomposition and reconstruction technique.
Detailed Description
The invention will be further described with reference to the drawings and examples.
The conventional noise reduction step by using wavelet decomposition and reconstruction technology is shown in fig. 1, the boundary continuation and interception of vectors are omitted, and in step 2, dh is a wavelet decomposition low-pass filter, dg is a wavelet decomposition high-pass filter, rh is a wavelet reconstruction low-pass filter, and Rg is a wavelet reconstruction high-pass filter are embodied. The method comprises the following specific steps:
Step 1: invoking noisy signals
The method is a first step of denoising by adopting wavelet decomposition and reconstruction technology, and can read the noisy signal under Matlab or other platforms to finish calling the noisy signal.
Step 2: wavelet decomposition of noisy signals to produce a matrix of wavelet coefficients
The two-dimensional noise-containing signal realizes wavelet decomposition by adopting a method of filtering in the horizontal direction and the vertical direction respectively, and four sub-images are generated in total, and the method is as follows:
(a) LL subband
The two-dimensional noise-containing signal is convolved by a wavelet decomposition low-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by a wavelet decomposition low-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain an approximate wavelet coefficient matrix CA of the image signal.
(B) HL sub-band
The two-dimensional noise-containing signal is convolved by a wavelet decomposition low-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by a wavelet decomposition high-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix CH of the image signal.
(C) LH sub-band
The two-dimensional noise-containing signal is convolved by a wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by a wavelet decomposition low-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix CV of the image signal.
(D) HH sub-band
The two-dimensional noise-containing signal is convolved by a wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by the wavelet decomposition high-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix CD of the image signal.
Step 3: thresholding high-frequency coefficients in three directions
(A) Setting a scale vector and a threshold vector
And (3) carrying out wavelet decomposition on the first wavelet, the second wavelet and the third wavelet of the noise-containing signal according to actual needs, wherein the scale vector is set according to the number of wavelet decomposition layers, and the threshold vector is set according to actual needs.
(B) Threshold filtering
Threshold filtering processing is respectively carried out on coefficient matrixes CA, CH, CV and CD of LL, HL, LH and HH sub-bands in three directions, and new coefficient matrixes NA, NH, NV and ND are correspondingly generated.
Step 4: signal wavelet reconstruction
The specific process of signal wavelet reconstruction is as follows:
(a) Approximate reconstruction coefficient matrix CA'
And after up-sampling and boundary extension are carried out on each column vector of the coefficient matrix NA of the image signal, convoluting with a wavelet reconstruction low-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convoluting with the wavelet reconstruction low-pass filter to complete interception of the row vector, so as to obtain an approximate reconstruction coefficient matrix CA' of the image signal.
(B) Reconstructing coefficient matrix CH'
And after up-sampling and boundary extension are carried out on each column vector of the coefficient matrix NH of the image signal, convoluting with a wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convoluting with a wavelet reconstruction low-pass filter to complete interception of the row vector to obtain a reconstruction coefficient matrix CH' of the image signal.
(C) Reconstructing coefficient matrix CV'
And after up-sampling and boundary extension are carried out on each column vector of the coefficient matrix NV of the image signal, convoluting with a wavelet reconstruction low-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convoluting with the wavelet reconstruction high-pass filter to complete interception of the row vector, so as to obtain a reconstruction coefficient matrix CV' of the image signal.
(D) Reconstructing coefficient matrix CD'
And after up-sampling and boundary extension are carried out on each column vector of the coefficient matrix ND of the image signal, convoluting with a wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convoluting with the wavelet reconstruction high-pass filter to complete interception of the row vector, so as to obtain a reconstruction coefficient matrix CD' of the image signal.
Step 5: post-noise reduction restoration of signals
Adding the approximate reconstruction coefficient matrix obtained in the step 4 to the reconstruction coefficient matrix to obtain a noise-reduced signal, namely: x ' =ca ' +ch ' +cv ' +cd '.
The step of denoising by wavelet decomposition and reconstruction technique is shown in fig. 2, and is omitted in fig. 2 because the boundary continuation and interception of the vector are unchanged, wherein: dh 'is a fractional wavelet decomposition low-pass filter, dg' is a fractional wavelet decomposition high-pass filter, rh 'is a fractional wavelet reconstruction low-pass filter, and Rg' is a fractional wavelet reconstruction high-pass filter. The technical scheme adopted by the invention for solving the technical problems comprises the following specific steps:
Step 1: invoking noisy signals
Reading the noise-containing signal under Matlab or other platforms, namely completing calling the noise-containing signal;
step 2: performing fractional wavelet decomposition on the noise-containing signal to generate a new wavelet coefficient matrix;
Firstly, fractional calculus changes are carried out on wavelet decomposition high-pass filter coefficients and low-pass filter coefficients, so that the filter form changes along with the change of the integral times of fractional calculus; secondly, the fractional wavelet decomposition high-pass filter coefficient and the low-pass filter after fractional calculus change are applied to the generation process of four sub-bands; the method comprises the following specific steps:
(a) LL subband;
after the boundary of the two-dimensional noise-containing signal in the horizontal direction is prolonged, carrying out convolution processing by using a fractional wavelet decomposition low-pass filter, carrying out downsampling on each row vector, after the boundary of the two-dimensional noise-containing signal in the vertical direction is prolonged, carrying out convolution processing by using the fractional wavelet decomposition low-pass filter, and carrying out downsampling on each column vector to obtain an approximate wavelet coefficient matrix FCA of the image signal;
(b) HL sub-band
After the two-dimensional noise-containing signal is prolonged at the boundary in the horizontal direction, performing convolution processing by using a fractional wavelet decomposition low-pass filter, performing downsampling on each row vector, and after the two-dimensional noise-containing signal is prolonged at the boundary in the vertical direction, performing convolution processing by using a fractional wavelet decomposition high-pass filter, performing downsampling on each column vector, and obtaining a wavelet coefficient matrix FCH of the image signal;
(c) LH sub-band
The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition low-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCV of the image signal;
(d) HH sub-band
The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCD of the image signal;
step 3: threshold processing is carried out on the high-frequency coefficients in three directions;
Thresholding the high frequency coefficients in the horizontal, diagonal, and vertical directions to generate new coefficient matrices FNA, FNH, FNV and FND;
Step 4: reconstructing signal wavelets;
Firstly, carrying out fractional calculus change on wavelet reconstruction high/low pass filter coefficients, changing the original fixed form, and enabling the filter form to change along with the change of the integral times of fractional calculus; secondly, a wavelet reconstruction high/low pass filter changed by a plurality of times of calculus is applied to the generation process of four reconstruction coefficient matrixes; the method comprises the following steps:
(a) Approximating the reconstruction coefficient matrix FCA';
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNA of the image signal, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete column vector interception, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction low-pass filter to complete row vector interception, so that an approximate reconstruction coefficient matrix FCA' of the image signal is obtained;
(b) Reconstructing coefficient matrix FCH'
And after up-sampling and boundary extension are carried out on each column vector of the coefficient matrix FNH of the image signal, convoluting with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convoluting with a fractional wavelet reconstruction low-pass filter to complete interception of the row vector, so as to obtain a reconstruction coefficient matrix FCH' of the image signal.
(C) Reconstructing coefficient matrix FCV'
And after up-sampling and boundary extension are carried out on each column vector of the coefficient matrix FNV of the image signal, convoluting with a fractional wavelet reconstruction low-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convoluting with a fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so as to obtain a reconstruction coefficient matrix FCV' of the image signal.
(D) Reconstructing coefficient matrix FCD'
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FND of the image signal, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCD' of the image signal is obtained;
step5: recovering after noise reduction of the signal;
Adding the approximate reconstruction coefficient matrix obtained in the step 4 to the reconstruction coefficient matrix to obtain a noise-reduced signal, namely: FX '=fca' +fch '+fcv' +fcd ', FX' is the resulting noise reduced signal.
The soft threshold algorithm is adopted to make fractional calculus change, so that the existing soft threshold algorithm is continuously changed along with the change of the integral times of fractional calculus, the processed signal is better adapted, and a better threshold filtering effect is achieved; the adopted soft threshold algorithm performs fractional calculus change; according to actual needs, carrying out wavelet first-layer wavelet decomposition, second-layer wavelet decomposition and three-layer wavelet decomposition on the noise-containing signal respectively, wherein the scale vector setting is determined by the number of wavelet decomposition layers, and the threshold vector is set according to actual needs; the coefficient matrices FCA, FCH, FCV and FCD of the LL, HL, LH, and HH subbands are respectively subjected to soft threshold filtering in the horizontal, diagonal, and vertical directions, to correspondingly generate new coefficient matrices FNA, FNH, FNV and FND.
(3) Technical defect of noise reduction by utilizing existing wavelet decomposition and reconstruction technology
At present, the defect of adopting a wavelet decomposition reconstruction technology to perform signal noise reduction processing is that the forms of a selected wavelet decomposition high/low pass filter and a reconstruction high/low pass filter are single and fixed, the form of a threshold algorithm is limited, and flexible adjustment cannot be performed according to actual signals, so that the noise reduction effect is limited.
Let x=x+40X randn (size (X)) be the noise-containing signal, where X is the Matlab system self-contained original image woman and 40X randn (size (X)) be the white noise signal applied. And (3) respectively carrying out one-layer, two-layer and three-layer decomposition on the noise-containing signal by utilizing a wavelet decomposition technology, carrying out filtering treatment on the high-frequency component by adopting a soft threshold value, wherein the threshold value vector is P, adopting a wavelet function name of sym5', and then carrying out wavelet reconstruction to finish the noise reduction treatment of the noise-containing signal. The processing result is divided into two parts: one part is an image simulation effect diagram, the other part is the maximum error value of the image after noise reduction compared with the original image, and the results are shown in fig. 3, fig. 4, fig. 5 and table 2 respectively.
As can be seen from the comparison of table 2 and table 1 and the comparison of (c) and (d) in fig. 3, 4 and 5, the noise reduction effect of the fractional wavelet decomposition and reconstruction technique is significantly better than that of the prior art. In addition, the values of lo_d and lo_r in table 2 are temporarily set to zero, that is, the number of times of integration of fractional calculus is zero, and if other values are selected, the noise reduction effect also has a rise space.
Table 2 maximum error contrast table relative to original image after fractional wavelet decomposition reconstruction
| Sequence number | N | P | Hi_D | Lo_D | Hi_R | Lo_R | V | Err1 | O |
| 1 | 1 | [34 50] | 0.808 | 0 | -0.2 | 0 | 0.25 | 121.63 | 16.9％ |
| 2 | 2 | [87 87] | 0.51 | 0 | 0.01 | 0 | 0.26 | 111.37 | 23.8％ |
| 3 | 3 | [97 97] | 0.10 | 0 | 0.11 | 0 | 0.01 | 117.37 | 20.3％ |
Wherein: number of N-wavelet decomposition layers
Hi_D-decomposition high pass filter fractional calculus integration times
Lo_D-decomposition low-pass filter fractional calculus integration times
Hi_R-reconstruction high pass filter fractional calculus integration times
Lo_R-reconstructed low-pass filter fractional calculus integration times
The number of times the V-soft threshold algorithm is integrated by fractional calculus
Err 1-noise reduction error value of fractional wavelet decomposition and reconstruction technology
O-precision improvement after noise reduction by fractional wavelet decomposition and reconstruction technique (error relative to Table 1)
The invention carries out fractional calculus change on the theoretical algorithm of the threshold value, so that the algorithm form of the threshold value is changed along with the change of the integral times of fractional calculus, and the algorithm form of the threshold value is greatly increased. Thus, the defect that the threshold algorithm is limited to a soft threshold value and a hard threshold value or other fixed forms is overcome. In addition, in order to further improve the noise reduction effect, the traditional noise reduction process by utilizing wavelet decomposition and reconstruction technology is improved.
Claims (2)
1. The noise reduction method by utilizing fractional wavelet decomposition and reconstruction technology is characterized by comprising the following steps:
Step 1: invoking noisy signals
Reading the noise-containing signal under Matlab or other platforms, namely completing calling the noise-containing signal;
step 2: performing fractional wavelet decomposition on the noise-containing signal to generate a new wavelet coefficient matrix;
Firstly, fractional calculus changes are carried out on wavelet decomposition high-pass filter coefficients and low-pass filter coefficients, so that the filter form changes along with the change of the integral times of fractional calculus; secondly, the fractional wavelet decomposition high-pass filter coefficient and the low-pass filter after fractional calculus change are applied to the generation process of four sub-bands; the method comprises the following specific steps:
(a) LL subband;
after the boundary of the two-dimensional noise-containing signal in the horizontal direction is prolonged, carrying out convolution processing by using a fractional wavelet decomposition low-pass filter, carrying out downsampling on each row vector, after the boundary of the two-dimensional noise-containing signal in the vertical direction is prolonged, carrying out convolution processing by using the fractional wavelet decomposition low-pass filter, and carrying out downsampling on each column vector to obtain an approximate wavelet coefficient matrix FCA of the image signal;
(b) HL sub-band
After the two-dimensional noise-containing signal is prolonged at the boundary in the horizontal direction, performing convolution processing by using a fractional wavelet decomposition low-pass filter, performing downsampling on each row vector, and after the two-dimensional noise-containing signal is prolonged at the boundary in the vertical direction, performing convolution processing by using a fractional wavelet decomposition high-pass filter, performing downsampling on each column vector, and obtaining a wavelet coefficient matrix FCH of the image signal;
(c) LH sub-band
The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition low-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCV of the image signal;
(d) HH sub-band
The two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the horizontal boundary is extended, each row vector is downsampled, the two-dimensional noise-containing signal is convolved by using a fractional wavelet decomposition high-pass filter after the vertical boundary is extended, and each column vector is downsampled to obtain a wavelet coefficient matrix FCD of the image signal;
step 3: threshold processing is carried out on the high-frequency coefficients in three directions;
Thresholding the high frequency coefficients in the horizontal, diagonal, and vertical directions to generate new coefficient matrices FNA, FNH, FNV and FND;
Step 4: reconstructing signal wavelets;
Firstly, carrying out fractional calculus change on wavelet reconstruction high/low pass filter coefficients, changing the original fixed form, and enabling the filter form to change along with the change of the integral times of fractional calculus; secondly, a wavelet reconstruction high/low pass filter changed by a plurality of times of calculus is applied to the generation process of four reconstruction coefficient matrixes; the method comprises the following steps:
(a) Approximating the reconstruction coefficient matrix FCA';
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNA of the image signal, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete column vector interception, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction low-pass filter to complete row vector interception, so that an approximate reconstruction coefficient matrix FCA' of the image signal is obtained;
(b) Reconstructing coefficient matrix FCH'
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNH of the image signal, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCH' of the image signal is obtained;
(c) Reconstructing coefficient matrix FCV'
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FNV of the image signal, convolution is carried out with a fractional wavelet reconstruction low-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCV' of the image signal is obtained;
(d) Reconstructing coefficient matrix FCD'
After up-sampling and boundary extension are carried out on each column vector of a coefficient matrix FND of the image signal, convolution is carried out with a fractional wavelet reconstruction high-pass filter to complete interception of the column vector, and after up-sampling and boundary extension are carried out on each row vector, convolution is carried out with the fractional wavelet reconstruction high-pass filter to complete interception of the row vector, so that a reconstruction coefficient matrix FCD' of the image signal is obtained;
step5: recovering after noise reduction of the signal;
Adding the approximate reconstruction coefficient matrix obtained in the step 4 to the reconstruction coefficient matrix to obtain a noise-reduced signal, namely: FX '=fca' +fch '+fcv' +fcd ', FX' is the resulting noise reduced signal.
2. The noise reduction method using fractional wavelet decomposition and reconstruction technique according to claim 1, wherein:
Step 3, adopting a soft threshold algorithm to perform fractional calculus change; the adopted soft threshold algorithm performs fractional calculus change; according to actual needs, carrying out wavelet first-layer wavelet decomposition, second-layer wavelet decomposition and three-layer wavelet decomposition on the noise-containing signal respectively, wherein the scale vector setting is determined by the number of wavelet decomposition layers, and the threshold vector is set according to actual needs; the coefficient matrices FCA, FCH, FCV and FCD of the LL, HL, LH, and HH subbands are respectively subjected to soft threshold filtering in the horizontal, diagonal, and vertical directions, to correspondingly generate new coefficient matrices FNA, FNH, FNV and FND.
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