CN105701781A - Image denoising method based on multi-resolution singular value decomposition - Google Patents

Abstract

The invention discloses an image denoising method based on multi-resolution singular value decomposition. The method comprises the following steps of step1, adjusting a size of an original image, and carrying out singular value decomposition on an adjusted image data matrix to acquire a left singular matrix; step2, carrying out product on a transposed matrix of the left singular matrix and the adjusted image data matrix to acquire a new image data matrix; step3, carrying out size adjusting on each row of data of the new image data matrix; step4, taking a low frequency portion as an original image and repeatedly carrying out at least once process from the step1 to the step3; step5, using a threshold denoising rule to process a matrix corresponding to a high frequency portion, recombining a processing result into the image data matrix with the same size with the original image and acquiring a denoised image. In the invention, when the noise is removed, simultaneously, high frequency information of the image can be well kept, and a process is simple and is easy to carry out.

Description

A kind of image de-noising method based on multiresolution singular value decomposition

Technical field

The present invention relates to Image Denoising Technology field, be specifically related to a kind of image de-noising method based on multiresolution singular value decomposition。

Background technology

Image, in the processes such as generation, transmission, storage, to be unavoidably subject to effect of noise, once image has noise, then not only its visual effect can be deteriorated, and the feature of itself also can be damaged。

Present digital camera generally generates image with CCD or CMOS, due to the duty that electronic component itself is undesirable, affect plus ambient light etc., cause that the image generated often has noise, and noise generally can be modeled with Gauss model or pulse by these noises。

In recent years, there had been substantial amounts of research work in image denoising field, it is proposed to carry out a lot of Denoising Algorithm, but Denoising Problems also exists always。For impulsive noise, medium filtering and its deformation, have been achieved for good denoising effect, the new method removing pulse signal that such as Rajamani et al. proposes in the recent period。Ravikishore et al. proposes a kind of based on quicksort, utilizes the Denoising Algorithm of boundary descriptor, and certainly the most known in recent years Denoising Algorithm is BM3D, and it combines the thought of non local denoising and transform domain, is current state-of-the-art Denoising Algorithm。

In existing denoising process, by more image texture information can be lost, the process of denoising lost the Partial Feature of image。

Summary of the invention

The invention provides a kind of image de-noising method based on multiresolution singular value decomposition, remove noise meanwhile, it is capable to retain the high-frequency information of image better, and process is simple, it is easy to implement。

A kind of image de-noising method based on multiresolution singular value decomposition, including:

Step 1, adjusts the size of original image, the image data matrix after adjusting is carried out singular value decomposition, obtains left singular matrix；

Step 2, carries out product by the image data matrix after the transposed matrix of left singular matrix and adjustment, obtains new image data matrix；

Step 3, carries out size adjusting to every data line of new image data matrix, wherein the low frequency part of the matrix correspondence original image after the first row data point reuse, the HFS of the matrix correspondence original image after remaining row data point reuse；

Step 4, using low frequency part as original image, repeats the process of step 1～step 3 at least one times；

Step 5, utilizes the matrix that threshold denoising rule treatments HFS is corresponding, result is reassembled into the image data matrix identical with original image size, namely obtains the image after denoising。

As preferably, in step 1, original image is of a size of M × N, is of a size of after adjustment

To being sized toImage data matrix carry out SVD singular value decomposition, obtain left singular matrix U after decomposition, be sized to 4 × 4, and the diagonal matrix S of centre, be sized to

As preferably, in step 3, by the size adjusting of the every data line in new image data matrix being

New image data matrix has four row data, LL, LH, HL and HH it is designated as successively from the first row to fourth line, the low frequency part of LL correspondence original image, the HFS of LH, HL and HH correspondence original image, takes out LL, as new original image, repeat the catabolic process of step 1～step 3, obtain new four matrix, new matrix also has four row data, the wherein low frequency part of the first row data correspondence original image, the HFS of remaining row data correspondence initial data。

As preferably, after utilizing the matrix that the complete HFS of threshold denoising rule treatments is corresponding, by corresponding adjustment of matrix beingVector, HFS and low frequency part are together to formMatrix, then do product with corresponding left singular matrix, obtain the image after denoising。

As preferably, in step 4, repeating the process of a step 1～step 3。

The present invention utilizes the method for MSVD that image is processed, and is equivalent to transform to image frequency domain, and noise is frequently found in HFS, so by HFS is filtered, threshold process in other words, it is possible to remove noise, in combination with the thought of multiresolution, complete denoising better。

Accompanying drawing explanation

Fig. 1 is the present invention flow chart based on the image de-noising method of multiresolution singular value decomposition。

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is described in detail。

As it is shown in figure 1, a kind of image de-noising method based on multiresolution singular value decomposition, comprise the steps:

(1) adjust the size of the noise image I that life size is M × N, become

When being embodied as, M=N=256, the picture size after adjustment is 4 × 16384, is designated as I₁。

(2) to I₁Carry out SVD decomposition:

[US]=SVD (I₁)

Wherein, SVD represents that singular value decomposition operates；U, S represent respectively final decompose obtain be sized to 4 × 4 left singular matrix and diagonal matrix, diagonal matrix diagonal entry is the singular value of descending, is sized to 4 × 16384。

(3) new matrix Y is calculated according to equation below:

Y=U^TI₁

Wherein, U is the left singular matrix that above-mentioned singular value decomposition obtains, the transposition operation of T representing matrix。

(4) take out the every a line in the above-mentioned matrix Y calculated, and adjust size:

$LL=Y\[0,:\].\mathrm{Re}shaper(\frac{M}{2},\frac{N)}{2}$

$LH=Y\[1,:\].\mathrm{Re}shaper(\frac{M}{2},\frac{N)}{2}$

$HL=Y\[2,:\].\mathrm{Re}shaper(\frac{M}{2},\frac{N)}{2}$

$HH=Y\[3,:\].\mathrm{Re}shaper(\frac{M}{2},\frac{N)}{2}$

Wherein, and Y [i :], the i-th row data of i=0,1,2,3 representing matrix Y, are a column vector；Reshape represents the operation adjusting size, is specially here and every data line of Y is adjusted to $\frac{M}{2}\×\frac{N}{2}=128\×128$ Size。

(5) take above-mentioned calculated LL matrix, repeat step (1)-(4), obtain four new matrixes, be designated as LL₀、LL₁、LL₂、LL₃, it is sized to (64,64)。

(6) with reference to the threshold value calculation method described in Nigam, Vaibhav, SajalLuthra, andSmritiBhatnagar. " Acomparativestudyofthresholdingtechniquesforimagedenoisi ng. " literary composition, to LL₁、LL₂、LL₃After carrying out threshold process, then again by LL₀、LL₁、LL₂、LL₃Adjustment becomes row vector, and synthesizes a new matrix L L_temp, formula is expressed as follows:

${\mathrm{LL}}_{temp}\[0,:\]={\mathrm{LL}}_0.\mathrm{Re}shape(1,\frac{MN}{4})$

${\mathrm{LL}}_{temp}\[1,:\]={\mathrm{LL}}_1.\mathrm{Re}shape(1,\frac{MN}{4})$

${\mathrm{LL}}_{temp}\[2,:\]={\mathrm{LL}}_2.\mathrm{Re}shape(1,\frac{MN}{4})$

${\mathrm{LL}}_{temp}\[3,:\]={\mathrm{LL}}_3.\mathrm{Re}shape(1,\frac{MN}{4})$

Wherein, LL_tempRepresent newly synthesized matrix, LL_temp[i :], i=0,1,2,3 represents LL_tempThe i-th row；Reshape represents the operation adjusting size, and M and N represents LL₀、LL₁、LL₂、LL₃Length and wide (LL₀、LL₁、LL₂、LL₃Length all identical with width)。

When being embodied as, M=N=64, it is about to be sized to the LL of (64,64)₀、LL₁、LL₂、LL₃It is adjusted to the row vector of (Isosorbide-5-Nitrae 096), is assigned to LL_temp, its correspondingly-sized is (4,4096)。

(7) new matrix L L is calculated according to equation below_new:

LL_new=U_tempLL_temp

Wherein, U_tempWhen LL matrix being carried out SVD operation corresponding to step (2), the left singular matrix obtained；LL_tempFor the newly synthesized matrix described in (6), LL_newWhen being embodied as, it is sized to (4,4096)。

Then again by LL_newSize is adjusted to (128,128), is designated as LL_de。

(8) same, LH, HL and HH are carried out threshold process, then as described in step (7) with LL_deAfter doing size adjusting together, synthesize new matrix, be designated as I₂, it is sized to (4,16384)。

(9) last, the image I after utilizing below equation to obtain denoising₃:

I₃=UI₂

Wherein, U is the left singular matrix described in step (2), I₂For the new composite matrix I obtained in step (8)₂。

When being embodied as, I₃It is sized to (4,16384), I the most at last₃Size adjusting is (256,256), obtains the image after final denoising。

The present embodiment carries out twice operation splitting, it is also possible to carry out repeatedly operation splitting as required, reach better denoising effect。

Claims (5)

1. the image de-noising method based on multiresolution singular value decomposition, it is characterised in that including:

Step 1, adjusts the size of original image, the image data matrix after adjusting is carried out singular value decomposition, obtains left singular matrix；

Step 2, carries out product by the image data matrix after the transposed matrix of left singular matrix and adjustment, obtains new image data matrix；

Step 3, carries out size adjusting to every data line of new image data matrix, wherein the low frequency part of the matrix correspondence original image after the first row data point reuse, the HFS of the matrix correspondence original image after remaining row data point reuse；

Step 4, using low frequency part as original image, repeats the process of step 1～step 3 at least one times；

Step 5, utilizes the matrix that threshold denoising rule treatments HFS is corresponding, result is reassembled into the image data matrix identical with original image size, namely obtains the image after denoising。

2. the image de-noising method based on multiresolution singular value decomposition as claimed in claim 1, it is characterised in that in step 1, original image is of a size of M × N, is of a size of after adjustment

3. the image de-noising method based on multiresolution singular value decomposition as claimed in claim 2, it is characterised in that in step 3, by the size adjusting of the every data line in new image data matrix be

4. the image de-noising method based on multiresolution singular value decomposition as claimed in claim 3, it is characterised in that after utilizing the matrix that the complete HFS of threshold denoising rule treatments is corresponding, by corresponding adjustment of matrix beVector, HFS and low frequency part are together to formMatrix, then do product with corresponding left singular matrix, obtain the image after denoising。

5. the image de-noising method based on multiresolution singular value decomposition as claimed in claim 4, it is characterised in that in step 4, repeat the process of a step 1～step 3。