CN103824262A - Improved rapid image restoration processing method using R-L iterative algorithm - Google Patents

Abstract

Disclosed is an improved rapid image restoration processing method using an R-L iterative algorithm. The method includes the steps that an image noise model is established, raw information of an observed image is acquired, and the information is given out in a matrix mode; the Gaussian kernel function is used as a point spread function, and an initial value is initialized to a restoration result of the observed image; numerical value iteration is carried out according to an iterative equation, and a final restored image is obtained after a plurality of times of iteration. According to the method, double regularization parameters are used, the Gaussian kernel function is used as the initial value, and the Alembert convergence criterion is used for conducting numerical value iteration in the iterative process; due to initial value selection, the operation efficiency is high, the iterative computation every time is more effective, and the number of iterations is greatly smaller than the number of iterations in an existing method; the method can be used for image restoration under the condition of high power noise, image fine details can be reserved, the luminance and the edge effect can be improved, the two regularization parameters can be flexibly selected, and the size of the point spread function is far smaller than the size of an original image.

Description

A kind of rapid image Recovery processing method of modified R-L iterative algorithm

Technical field

The invention belongs to technical field of image processing, particularly a kind of rapid image Recovery processing method of modified R-L iterative algorithm.

Background technology

Image in fields such as medical treatment, astronomy, remote sensing has very high requirement for identification and sharpness, and larger but actual reception image is subject to noise effect, overriding noise type is poisson noise.At present, that relatively more conventional is R-L(Richardson-Lucy) iterative algorithm, but due to the ill characteristic with matrix inversion wherein, so have some technical schemes to propose the method for regularization, what some regularization method adopted is one-parameter regularization, cannot utilize well so each iterative process to realize calculating rapidly and efficiently, what some regularization adopted is the iterative process of partial differential equation, its arithmetic speed is slow, and complexity is high, high to the hardware requirement of calculating process.

Summary of the invention

In order to overcome the shortcoming of above-mentioned prior art, the object of the present invention is to provide a kind of rapid image Recovery processing method of modified R-L iterative algorithm, utilize biregular parameter, adopt gaussian kernel function as initial value, in iterative process, use and reach bright Bel's convergence criterion and carry out numerical value iteration.

To achieve these goals, the technical solution used in the present invention is:

A rapid image Recovery processing method for modified R-L iterative algorithm, sets up image noise model i=h*o+n, and wherein i is the image observing, and h is point spread function, and o is real image, and n is noise, and process comprises the steps:

Step 1. obtains the raw information of the image observing, and provides in the mode of matrix;

Step 2. is used gaussian kernel function for point spread function h and the image restoration result i initialize observing;

Step 3. is carried out numerical value iteration according to following two iterative equations:

$o^{(m+1)}=\frac{i\left(s\right)}{(o^{\left(m\right)}*h)}*h^{*}\left(s\right)\·\frac{o^{\left(m\right)}}{(1-{\mathrm{\λ}}_1\·\mathrm{div}\left(\frac{{\▿o}^{\left(m\right)}}{\left|\right|{\▿o}^{\left(m\right)}\left|\right|}\right))}$

$h^{(m+1)}=\frac{i\left(s\right)}{(h^{\left(m\right)}*o)\left(s\right)}*o^{*}\left(s\right)\·\frac{h^{\left(m\right)}}{({\mathrm{\Σ}}_{s}o\left(s\right)-{\mathrm{\λ}}_2\·\mathrm{div}\left(\frac{{\▿h}^{\left(m\right)}}{{\▿h}^{\left(m\right)}}\right))}$

In formula, the region at s presentation video place, m is iterations, o ^(m)represent the result of the o of the m time iteration, h ^(m)the result that represents the h of the m time iteration, * represents convolution algorithm, represents multiplying, o ^*and h ^*represent respectively the conjugation of o and h, λ ₁and λ ₂represent regularization parameter, be constant, Σ _so (s) is illustrated in the numerical value summation to o in whole image-region, and div () represents the variable in bracket to ask divergence computing,

represent gradient operator, || || represent norm;

In iterative process, adopt alternately iteration, first use o ^(m)and h ^(m)iteration obtains o ^(m+1), re-use o ^(m+1)and h ^(m)obtain h ^(m+1), or first use o ^(m)and h ^(m)iteration obtains h ^(m+1), re-use h ^(m+1)and o ^(m)obtain o ^(m+1);

Through the o obtaining after several times iteration ^(m)the i.e. final image recovering.

In described step 1, if original image is gray scale image, be single matrix; If original image is coloured image, is divided into tri-components of RGB and processes respectively.

In described step 1, described matrix is the picture element matrix of the image that observes.

In described step 2, use gaussian kernel function, provide its size and standard deviation, can complete for the initialized assignment of point spread function, re-use this point spread function and carry out convolution one time with the image receiving, can complete for the initialization assignment of wanting the true picture recovering.

In described step 3, the data scale of h is far smaller than the data scale of i and o, and data scale refers to the size of matrix.

In described step 3, the region at image place is two-dimensional coordinate region.

The numerical value of iterations n is generally no more than 10.

Compared with prior art, beneficial effect of the present invention is that advantage is:

Initial value choose high, the each iterative computation of the operation efficiency causing more effectively, iterations is significantly less than existing method, can use this method to carry out image recovery under compared with very noisy condition, can retain image fine detail, promote brightness and edge effect, two regularization parameters are chosen very flexibly, the size of point spread function is far smaller than the size of original image.

Accompanying drawing explanation

Fig. 1 is the original image of the moonscape of spacecraft camera.

Fig. 2 is the enlarged drawing of oval part in Fig. 1.

Fig. 3 uses the present invention to carry out the result figure after iterative processing Fig. 2.

Embodiment

Describe embodiments of the present invention in detail below in conjunction with drawings and Examples.

As shown in Figure 1, be the original image of the moonscape of spacecraft camera.Process from wherein intercepting a part, as shown in Figure 2, it is very fuzzy as seen for cut-away view picture, luminance shortage, and it is the image i observing.

Utilize image Recovery processing method of the present invention, set up image noise model i=h*o+n, wherein i is the image observing, i.e. Fig. 2, and h is point spread function, is of a size of 15 × 15; O is real image, is the object that finally will solve, and n is noise, and process comprises the steps:

Step 1. obtains the raw information of the image i observing, provides in the mode of matrix, if original image is gray scale image, be single matrix; If original image is coloured image, is divided into tri-components of RGB and processes respectively.The image that the present embodiment observes is for colored, and the line number of this matrix and columns equal respectively the height and width of image pixel, and each element of matrix equals the numerical value of image correspondence position pixel.

Step 2. is used gaussian kernel function, provides its size and standard deviation, is point spread function h and the image restoration result i initialize observing; Re-use this point spread function and carry out convolution one time with the image receiving, can complete for the initialization assignment of wanting the true picture recovering.In the present embodiment, choose gaussian kernel function and be of a size of 15, standard deviation is 2.

The associating deconvolution formula of step 3. based on maximum a posteriori probability is as follows:

$p\left(i\right|o,h)=\underset{s}{\mathrm{\Π}}\left(\frac{{(h*o)\left(s\right)}^{i\left(s\right)}\exp (-(h*o)\left(s\right))}{i\left(s\right)!}\right)$

The likelihood maximum of taking the logarithm:

$J(o,h)=\underset{s}{\mathrm{\Σ}}((h*o)\left(s\right)-i\left(s\right)\log \left((h*o)\left(s\right)\right))$

It is carried out to the regularization based on total variation:

$J(o,h)=\underset{s}{\mathrm{\Σ}}((h*o)\left(s\right)-i\left(s\right)\log \left((h*o)\left(s\right)\right))+{\mathrm{\λ}}_1\left|\right|\▿o\left|\right|+{\mathrm{\λ}}_2\left|\right|\▿h\left|\right|$

Above formula is got variation to o and h respectively, can obtain:

$1-\frac{i\left(s\right)}{(o*h)\left(s\right)}*h^{*}\left(s\right)-{\mathrm{\λ}}_1\·\mathrm{div}\left(\frac{\▿o}{|\▿o|}\right)0$

$(1-\frac{i\left(s\right)}{(o*h)\left(s\right)})*o^{*}\left(s\right)\·-{\mathrm{\λ}}_2\·\mathrm{div}\left(\frac{\▿h}{|\▿h|}\right)=0$

To reaching bright Bel's convergence iteration above, there are following two formulas (for iteration time):

$o^{(m+1)}=\frac{i\left(s\right)}{(o^{\left(m\right)}*h)}*h^{*}\left(s\right)\·\frac{o^{\left(m\right)}}{(1-{\mathrm{\λ}}_1\·\mathrm{div}\left(\frac{{\▿o}^{\left(m\right)}}{\left|\right|{\▿o}^{\left(m\right)}\left|\right|}\right))}$

$h^{(m+1)}=\frac{i\left(s\right)}{(h^{\left(m\right)}*o)\left(s\right)}*o^{*}\left(s\right)\·\frac{h^{\left(m\right)}}{({\mathrm{\Σ}}_{s}o\left(s\right)-{\mathrm{\λ}}_2\·\mathrm{div}\left(\frac{{\▿h}^{\left(m\right)}}{{\▿h}^{\left(m\right)}}\right))}$

In formula, the region at s presentation video place (for example two-dimensional coordinate region), m is iterations, o ^(m)represent the result of the o of the m time iteration, h ^(m)the result that represents the h of the m time iteration, * represents convolution algorithm, represents multiplying, o* and h* represent respectively the conjugation of o and h, λ ₁and λ ₂represent regularization parameter, be constant, the selection range of total variation parameter is larger, can choose according to the intensity of actual noise, and the present embodiment is chosen λ ₁=0.1, λ ₂=0.03, Σ _so (s) is illustrated in the numerical value summation to o in whole image-region, and div () represents the variable in bracket to ask divergence computing,

represent gradient operator, || represent norm;

In iterative process, adopt alternately iteration, first use o ^(m)and h ^(m)iteration obtains o ^(m+1), re-use o ^(m+1)and h ^(m)obtain h ^(m+1), or first use o ^(m)and h ^(m)iteration obtains h ^(m+1), re-use h ^(m+1)and o ^(m)obtain o ^(m+1); Wherein the data scale of h can be far smaller than the data scale of i and o, and data scale refers to the size of matrix.

The o of the present embodiment through obtaining after 7 iteration ⁽⁷⁾the i.e. final image recovering, as shown in Figure 3, its brightness and sharpness have all had very large lifting to the result after iteration as seen.

Claims (7)

1. a rapid image Recovery processing method for modified R-L iterative algorithm, is characterized in that, sets up image noise model i=h*o+n, and wherein i is the image observing, and h is point spread function, and o is real image, and n is noise, and process comprises the steps:

Step 1. obtains the raw information of the image observing, and provides in the mode of matrix;

Step 2. is used gaussian kernel function for point spread function h and the image restoration result i initialize observing;

Step 3. is carried out numerical value iteration according to following two iterative equations:

$o^{(m+1)}=\frac{i\left(s\right)}{(o^{\left(m\right)}*h)}*h^{*}\left(s\right)\·\frac{o^{\left(m\right)}}{(1-{\mathrm{\λ}}_1\·\mathrm{div}\left(\frac{{\▿o}^{\left(m\right)}}{\left|\right|{\▿o}^{\left(m\right)}\left|\right|}\right))}$

$h^{(m+1)}=\frac{i\left(s\right)}{(h^{\left(m\right)}*o)\left(s\right)}*o^{*}\left(s\right)\·\frac{h^{\left(m\right)}}{({\mathrm{\Σ}}_{s}o\left(s\right)-{\mathrm{\λ}}_2\·\mathrm{div}\left(\frac{{\▿h}^{\left(m\right)}}{{\▿h}^{\left(m\right)}}\right))}$

In formula, the region at s presentation video place, m is iterations, o ^(m)represent the result of the o of the m time iteration, h ^(m)the result that represents the h of the m time iteration, * represents convolution algorithm, represents multiplying, o ^*and h ^*represent respectively the conjugation of o and h, λ ₁and λ ₂represent regularization parameter, be constant, Σ _so (s) is illustrated in the numerical value summation to o in whole image-region, and div () represents the variable in bracket to ask divergence computing, represent gradient operator, || || represent norm;

In iterative process, adopt alternately iteration, first use o ^(m)and h ^(m)iteration obtains o ^(m+1), re-use o ^(m+1)and h ^(m)obtain h ^(m+1), or first use o ^(m)and h ^(m)iteration obtains h ^(m+1), re-use h ^(m+1)and o ^(m)obtain o ^(m+1);

Through the o obtaining after several times iteration ^(m)the i.e. final image recovering.

2. the rapid image Recovery processing method of modified R-L iterative algorithm according to claim 1, is characterized in that, in described step 1, if original image is gray scale image, is single matrix; If original image is coloured image, is divided into tri-components of RGB and processes respectively.

3. the rapid image Recovery processing method of modified R-L iterative algorithm according to claim 1, is characterized in that, in described step 1, described matrix is the picture element matrix of the image that observes.

4. the rapid image Recovery processing method of modified R-L iterative algorithm according to claim 1, it is characterized in that, in described step 2, use gaussian kernel function, provide its size and standard deviation, can complete for the initialized assignment of point spread function, re-use this point spread function and carry out convolution one time with the image receiving, can complete for the initialization assignment of wanting the true picture recovering.

5. the rapid image Recovery processing method of modified R-L iterative algorithm according to claim 1, is characterized in that, in described step 3, the data scale of h is far smaller than the data scale of i and o, and data scale refers to the size of matrix.

6. the rapid image Recovery processing method of modified R-L iterative algorithm according to claim 1, is characterized in that, in described step 3, the region at image place is two-dimensional coordinate region.

7. the rapid image Recovery processing method of modified R-L iterative algorithm according to claim 1, is characterized in that, in described step 3, the numerical value of iterations n is not more than 10.

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