CN111489307B - Image PSF deconvolution method based on difference correction term - Google Patents

Abstract

The invention discloses an image PSF deconvolution method based on a difference correction term, which is characterized by comprising the additive difference correction term, wherein the correction term is the correlation between the difference of the PSF on the convolution of an observation result and a current result and the PSF, or the transpose matrix of the PSF on the convolution of the observation result and the current result. The method (PSFdeDCT) is an improvement on a Lucy-Richardson algorithm PSFdeLR based on maximum likelihood estimation, and successfully avoids various defects of the PSFdeLR algorithm, including such as 1) the image pixel value cannot be negative, 2) ringing effect caused by image edge oscillation and the like, and in addition, the PSFdeDCT technology is not only suitable for the cypress distribution but also suitable for the non-cypress distribution image, and the speed is slightly faster than that of the existing PSFdeLR algorithm.

Description

Image PSF deconvolution method based on difference correction term

Technical Field

The invention relates to the technical field of image processing, in particular to an image PSF deconvolution method based on a difference correction term.

Background

In the field of Point Spread Function (PSF) deconvolution of images, a number of approaches have been developed: such as the Lucy-Richardson image PSF deconvolution technology based on maximum likelihood estimation and regularization means added on the basis of the technology, such as the Winner filter PSF deconvolution technology based on the least mean square error or least square method principle, and further such as the PSF deconvolution technology based on entropy maximization, etc. The Lucy-Richardson image PSF deconvolution technology (LR technology) based on maximum likelihood estimation has great development prospect in the days of more mature computer technology, and the main advantages include: 1) The cypress noise can be treated naturally, which is very suitable for some practical situations; 2) The calculation speed is faster. The main disadvantages are: 1) Where the pixel value is negative, the pixel value cannot be used, and in actual situations, the pixel value of the image tends to be negative after the background is subtracted; 2) Edge ringing is serious; 3) Since the formula of the LR technique is based on maximum likelihood estimation, obtained by assuming a cypress distribution, the technique is theoretically unsuitable for the case of non-cypress distribution.

Disclosure of Invention

Aiming at the problems existing in the prior art, the invention provides an image PSF deconvolution technology based on a difference correction term: PSFdeDCT can overcome the defects of the prior art and realize more effective image PSF deconvolution.

The technical scheme provided by the invention comprises the following two steps:

scheme one:

a method for deconvolution of an image PSF based on a difference correction term, characterized by the addition of the difference correction term, the correction term being a correlation of the difference in PSF over the convolution of the observed result with the current result and the PSF:

wherein x, y represent pixel coordinate positions, f _i (x, y) is the result of the ith iteration, i is an integer, f _i+1 (x, y), i.e., the result of the (i+1) th iteration, g (x, y) is the observed image, h (x, y) is the point spread function PSF,

is a convolution symbol and is a correlation symbol.

When i is an initial value of 0, an initial value f of the iteration ₀ (x, y) is g (x, y).

Scheme II:

an image PSF deconvolution method based on a difference correction term, characterized by the difference correction term with additivity, the correction term being a transpose matrix of a difference deconvolution PSF of a PSF on a convolution of an observation and a current result:

wherein x, y represent pixel coordinate positions, f _i (x, y) is the result of the ith iteration, i is an integer, f _i+1 (x, y), i.e., the result of the (i+1) th iteration, g (x, y) is the observed image, h (x, y) is the point spread function PSF,

is a convolution symbol, h (x, y) ^T Is the transposed matrix of h (x, y).

When i is an initial value of 0, an initial value f of the iteration ₀ (x, y) is g (x, y).

The beneficial effects are that:

the invention is based on the image PSF deconvolution method (PSFdeDCT) of the difference correction term, and does not need to bear the image divergence caused by the fact that the denominator tends to 0 or the pixel negative value, and the additive difference correction term has the balance effect of counteracting negative feedback, so that the image with negative value pixels and the non-cypress distribution image can be processed, the reconstruction effect on the image edge is much better than PSFdeLR, and the processing speed is also faster than PSFdeLR.

Drawings

FIG. 1, top right, is an elliptical Gaussian PSF with a ratio of the major to minor axes of 3:1, top left is a simulated image obtained by convolving Miss Lena real image (pixel range-67-233) of 511pixel in the top PSF, bottom left is the result of PSFdelr after 40 iterations, and bottom right is the result of PSFdeDCT after 40 iterations;

FIG. 2, top left is Miss Lena real image (pixel value range 33-333), top right is a simulated image obtained by convolving the real image with the PSF of the top right of FIG. 1, bottom left is the result of PSFdelR after 800 iterations, and bottom right is the result of PSFdeDCT after 800 iterations.

Detailed Description

In order to clarify the technical scheme and effect of the present invention, the present invention will be further described with reference to specific examples and effect comparison diagrams.

Scheme one:

the Lucy-Richardson method of deconvolution of PSF for a single image (Point spread function deconvolution based on Lucy-Richardson algorithm, PSFdelr) is derived from the derivation of the maximum likelihood estimate, with the iterative formula:

wherein (x, y) represents the pixel coordinate position, typically an integer, f _i (x, y) is the result of the ith iteration, g (x, y) is the observed image, h (x, y) is the point spread function PSF,

is a convolution symbol and is a correlation symbol.

It can be seen that the right end of the above iterative formula is a ratio correction term multiplied by the last iteration result, the correction term being multiplicative. The ratio correction term here is why the three drawbacks listed above are that a pixel close to 0 in the denominator in the correction term will cause the surrounding image to fluctuate drastically to diverge, as in fig. 1, and the edge effect of the image is also iteratively amplified (negative feedback) by the multiplicative correction term, causing ringing (ringing) phenomenon, as in fig. 2.

We make a change to LR iteration equation (1) above, obtaining the following equation:

wherein x, y represent the coordinate position of the pixel in the image, typically an integer, f _i (x, y) is the result of the ith iteration, f _i+1 (x, y), i.e., the result of the (i+1) th iteration, g (x, y) is the observed image, h (x, y) is the point spread function PSF,

is a convolution symbol and is a correlation symbol.

In the formula (2), i is an integer, the value is taken from 0, and when i is an initial value 0, the initial value f of iteration is taken ₀ (x, y) is g (x, y). The observation image can be chosen as the initial value f of the iteration when we have no more information about the result ₀ (x, y), f ₀ (x, y) is carried into the formula (2) and calculated to obtain f ₁ (x, y), the result of the first iteration, followed by a loop iteration operation using (2) until the desired result is reached.

In this wayThe right end of the iterative formula is a difference correction term plus the last iterative result f _i The correction term is additive (x, y), which has the advantage that: there is no concern about image divergence caused by denominator tending to 0 or pixel negative values; the additive difference correction term has a balancing effect that counteracts the negative feedback.

Comparing equations (1) and (2) shows that the PSFdeDCT of the present invention has two more addition operations and one less division and one multiplication operation than the existing PSFdeLR, and thus the PSFdeDCT has a faster speed than the PSFdeLR.

Example 1:

we convolve a 3:1 ratio of major to minor elliptic gaussian PSF (fig. 1, top right) with a Miss Lena real image of size 511×511pixel (pixel range-67-233) to obtain a simulated observation image (fig. 1, top left), it being apparent that the observation image is blurred after convolving the PSF. Because the pixels have negative values, the psfderl has a strong oscillation after several iterations, and as the number of iterations increases, the oscillating pixels drive surrounding pixels to diverge, as shown in fig. 1, bottom left. However, PSFdeDCT well avoids this problem, the pixels in the image are trend converging, and the PSF deconvolution iteration proceeds smoothly, as in fig. 1, bottom right.

Example 2:

we add 100 to the pixel values of the Miss Lena real image of example 1 (FIG. 2, top left, pixel range adjusted to 33-333), then convolve with an elliptical Gaussian PSF with a 3:1 ratio of major to minor axes (FIG. 1, top right) to obtain a simulated observation image (FIG. 2, top right). In this case, the simulated observation image has no negative value, so that the psfderlr can work normally, but the ringing phenomenon of the image edge is serious, particularly along the main axis direction of the PSF, the oscillation is strongest, and after 800 iterations, the upper and lower edges lose half of information (fig. 2, lower left). While the deconvolution capability of the psfdec is excellent even at the edges, efficiently restoring the detail information at the edges (fig. 2, bottom right). After the same number of iterations at the non-edges, the psfderl is as effective as PSFdeDCT.

The method can develop corresponding PSFdeDCT software based on the C language, and the software can carry out PSF deconvolution according to the input observation image, PSF and the iteration times required by a user, and output the deconvoluted image with the same size.

Scheme II:

unlike the first scheme, the additive difference correction term in the first scheme is a transpose matrix of a difference deconvolution PSF of a PSF on convolution of an observation result and a current result, and the specific formula is as follows:

wherein, x and y represent pixel coordinate positions, the value is an integer, f _i (x, y) is the result of the ith iteration, i is an integer, f _i+1 (x, y), i.e., the result of the (i+1) th iteration, g (x, y) is the observed image, h (x, y) is the point spread function PSF,

is a convolution symbol, h (x, y) ^T Representing the transposed matrix of the PSF.

When i is an initial value of 0, an initial value f of the iteration ₀ (x, y) is g (x, y).

Experiments prove that compared with the PSFdelr in the prior art, the scheme has excellent image processing capability.

The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the foregoing embodiments, which have been described in the foregoing embodiments and description merely illustrates the principles of the invention, and various changes and modifications may be made therein without departing from the spirit and scope of the invention, the scope of which is defined in the appended claims, specification and their equivalents.

Claims (2)

1. A method for deconvolution of an image PSF based on a difference correction term, characterized by the addition of the difference correction term, the correction term being a correlation of the difference in PSF over the convolution of the observed result with the current result and the PSF:

wherein x, y represent pixel coordinate positions, f _i (x, y) is the result of the ith iteration, i is an integer, f _i+1 (x, y), i.e., the result of the (i+1) th iteration, g (x, y) is the observed image, h (x, y) is the point spread function PSF,

is a convolution symbol, is a correlation symbol;

when i is an initial value of 0, an initial value f of the iteration ₀ (x, y) is g (x, y);

and performing PSF deconvolution according to the input observation image, PSF and the iteration number required by the user, and outputting deconvoluted images with the same size.

2. An image PSF deconvolution method based on a difference correction term, characterized by the difference correction term with additivity, the correction term being a transpose matrix of a difference deconvolution PSF of a PSF on a convolution of an observation and a current result:

wherein x, y represent pixel coordinate positions, f _i (x, y) is the result of the ith iteration, i is an integer, f _i+1 (x, y), i.e., the result of the (i+1) th iteration, g (x, y) is the observed image, h (x, y) is the point spread function PSF,

is a convolution symbol, h (x, y) ^T Is the transposed matrix of h (x, y);

when i is an initial value of 0, an initial value f of the iteration ₀ (x, y) is g (x, y);

and performing PSF deconvolution according to the input observation image, PSF and the iteration number required by the user, and outputting deconvoluted images with the same size.

Images