Digital image restoration based on pixel simultaneous detection probabilities

TL;DR

This paper introduces a novel image restoration method based on pixel simultaneous detection probabilities (PSDP), utilizing matrix equations and Gaussian elimination to improve image quality, especially in mammography images, with high precision even in noisy conditions.

Contribution

The paper presents a new image restoration algorithm based on PSDP and matrix solutions, demonstrating its effectiveness on simulated and real mammography images.

Findings

Restoration accuracy better than 3% with PSDP-based method.

Effective noise handling in image restoration.

Improved spatial resolution demonstrated on absorber edge image.

Abstract

Here an image restoration on the basis of pixel simultaneous detection probabilities (PSDP) is proposed. These probabilities can be precisely determined by means of correlations measurement [NIMA 586 (2008) 314-326]. The proposed image restoration is based on the solution of matrix equation. Non-zero elements of Toeplitz block matrix with ones on the main diagonal, is determined using PSDP. The number of non zero descending diagonals depends on the detector construction and is not always smaller than 8. To solve the matrix equation, the Gaussian elimination algorithm is used. The proposed restoration algorithm is studied by means of the simulated images (with and without additive noise using PSDP for General Electric Senographe 2000D mammography device detector) and a small area (160x160 pixels) of real images acquired by the above mentioned device. The estimation errors of PSDP and the additive noise magnitude permits to restore images with the precision better than 3% for the above mentioned detector. The additive noise in the real image is present after restoration and almost has the same magnitude. In the restored small area (16x16 mm) of real images, the pixel responses are not correlated. The spatial resolution improvement is also analyzed by the image of an absorber edge.