Image-processing system and image-processing program
An image deteriorated by camera shake, or the like, is restored in a short period of time. A ∇J computation section computes an evaluation value J from a deteriorated image G captured by means of photographing, a restored image F, and a PSF computed from an angular velocity detected by an angular velocity sensor, and further computes ∇J. When the square of norm of ∇J exceeds a threshold value, there is iterated processing for computing a new, restored image F by means of subtracting ε·∇J from the restored image F. A convergence parameter computation section sets the convergence parameter ε as a value which first shows an increase and subsequently a decrease depending on the number of iterations, thereby increasing the speed of convergence and inhibiting divergence.
1. A computer program product for restoring an image F by means of a deterioration function H determined from a captured, deteriorated image G and image-capture conditions, the computer program product comprises a computer readable storage medium having a program stored thereon for performing the steps of:
(a) computing, as an evaluation value J, a difference between the deteriorated image G and an image HF acquired by subjecting the image F to the deterioration function H and which repeatedly performs processing for computing the image F and the evaluation value J until a gradient of the evaluation value J is the threshold value or less; and
(b) setting a convergence parameter multiplied by the gradient to thus adjust the number of iteration operations and sets the convergence parameter to a value which shows an increase and subsequently a decrease with an increase in the number of iterations.
2. The computer program product according to claim 1 , wherein step (a) computes a new image F by computing a difference between the image F and a value which has been determined by multiplication of the gradient by the convergence parameter.
3. The computer, program product according to claim 1 , wherein step (b) sets the convergence parameter as a function of the number of iterations.
4. The computer program product according to claim 1 , wherein step (b) sets the convergence parameter by use of a product of an increasing function which increases a value depending on the number of iterations and a decreasing function which decreases a value depending on the number of iterations.
5. The computer program product according to claim 4 , wherein step (b) sets the convergence parameter, by means of multiplying a constant α by an inverse of square of the gradient and additionally multiplying by a decreasing function that decreases a value depending on the number of iterations.
6. The computer program product according to claim 5 , wherein step (b) sets the convergence parameter, by means of multiplying the constant α by the inverse of square of the gradient and additionally multiplying by the decreasing function that leads to y=C−A n/B , provided that n denotes the number of iterations and A, B, and C denote positive real numbers.
7. The computer program product according to claim 6 , wherein at least any of the constants A, B, and C is set in accordance with a matrix size of the deterioration function H.
8. A computer program product for restoring an image F by means of a deterioration function H determined from a captured, deteriorated image G and image-capture conditions by means of iterative operations complying with a steepest-descent method, the computer program product comprises a computer readable storage medium having a program stored thereon for performing the steps of:
(a) storing the deteriorated image G;
(b) storing the restored image F;
(c)computing the deterioration function H;
(d) computing an evaluation value J from the deteriorated image G, the restored image F, and the deterioration function according to J=∥G−HF∥ 2 and further computes ∇J corresponding to a gradient of the evaluation value J;
(e) computing a square of norm of ∇J;
(f) comparing the square of norm of ∇J with a threshold value;
(g) outputting, as a restoration-completed image, the restored image F when the square of norm of ∇J is the threshold value or less, computes a new restored image F by means of subtracting, from the restored image F, a value determined by multiplication of ∇J by the convergence parameter ε when a square of norm of ∇J exceeds a threshold value, and stores the restored image in the second storage means in an updating manner; and
(h) computing the convergence parameter ε as a value which shows an increase and subsequently a decrease depending on the number of iterations.
9. The computer program product according to claim 8 , wherein the step (h) computes the convergence parameter ε by use of the square of norm of ∇J.
10. The computer program product according to claim 8 , wherein step (h) computes the convergence parameter ε by use of the square of norm of ∇J and a coefficient which monotonously decreases depending on the number of iteration operations.
11. An image-processing computer program product for causing a computer to perform processing for restoring an image F by means of a deterioration function H determined from a captured, deteriorated image G and image-capture conditions by means of iterative operations complying with a steepest-descent method, the computer program product comprises a computer readable storage medium having a program stored thereon for performing the steps of:
(a) a step of computing the evaluation value J from the deteriorated image G, the restored image F, and the deterioration function according to
J=∥G−HF∥ 2 .
(b) a step of computing ∇J corresponding to a gradient of the evaluation value J;
(c) a step of computing a square of norm of ∇J;
(d) a step of comparing the square of norm of ∇J with a threshold value;
(e) a step of computing, when the square of norm of ∇J exceeds the threshold value, a new restored image F by means of subtracting a value determined by multiplication of ∇J by the convergence parameter ε from the restored image F; and
(f) a step of repeatedly performing processing pertaining to (a) to (e) until the square of norm of ∇J is the threshold value or less, wherein the convergence parameter ε is a value which shows an increase and subsequently a decrease depending on the number of iteration operations.
12. The image-processing computer program product according to claim 11 , further comprising:
(g) a step of computing the convergence parameter ε by multiplying a predetermined coefficient α by an inverse of the square of norm of ∇J and additionally by a coefficient which monotonously decreases depending on the number of iterations.