A Restoration Method of Degraded Images using Factorization of Polynomials
Takashi Ozeki, Eiji Watanabe, Hiroshi Ishikawa, Fujio Kobayashi · Institutional Repositories DataBase (IRDB) · 2003
Usually, observed images are degraded and represented by the convolution of two signals. Here, one is an original image and the other is a point spread function (PSF) which causes degradation of original images. Blind deconvolution (BD) is the problem to estimate an original image and a PSF from only a degraded image. If we have no restriction condition to signals, we can not determine a pair of two signals. Because this problem sometimes has many solutions and, in the worst case, has infinite solutions. Nevertheless, almost everyone does not discuss this indeterminate property. In this paper, we show that BD has only finite solutions if an original image and a PSF are nonzero over a restricted domain, in other words, an observed image has finite support. Then we propose an algorithm to find all finite solutions under this boundary condition. The key of the proof is to use z transformation and factorization of polynomials. Moreover, we give a sufficient condition in which BD has only one solution. Finally we confirm that we can extract all sets of an original image and a PSF from a degraded image by using our algorithm in numerical examples.