Optimal stopping condition for iterative image deconvolution by new orthogonality criterion

Abstract

The stopping condition is a common problem for non-regularized deconvolution methods. We introduce an automatic procedure for estimating the ideal stopping point based on a new measure of independence, checking an orthogonality criterion of the estimated signal and its gradient at a given iteration. We provide an effective lower bound estimate than the conventional ad-hoc methods, proving its superiority to the others at a wide range of different noise models.Introduction: Blurring is a common issue in almost all image acquisition processes.

Adaptive Image Decomposition into Cartoon and Texture Parts Optimized by the Orthogonality Criterion

“…In this section, we shortly summarize published results closely related to the proposed method: non-linear filtering is introduced in [5], Anisotropic Diffusion in [14]- [16] and measures of independence in [12], [17], [18]. 1) BLMV Nonlinear Filter: Buades et al have recently proposed a non-linear method inspired by eq.…”

“…3) The Use of Independence in Image Decomposition: The independence of the carton part and the texture/noise part of the image was used in denoising, decomposition [12] and restoration [18] algorithms.…”

“…In [18], the Angle Deviation Error (ADE) -introduced in [17] -is used as a measure of independence to automatically find the best stopping point for an iterative non-regularized image deconvolution method. As the deconvolution problem is ill-posed, after a certain point, further iterations will only amplify the noise on the estimated image.…”

“…As the deconvolution problem is ill-posed, after a certain point, further iterations will only amplify the noise on the estimated image. The heart of the method in [18] is to find the iteration, where the change of the estimated image in one time step X(t) − X(t − 1), and the estimated image itself (X(t)) are the most independent of each other. The described ADE measure is somewhat similar to correlation [12], but it is based on the pure orthogonality of two image partitions (e.g.…”

Parametric Blind Image Deblurring With Gradient Based Spectral Kurtosis Maximization

“…A variety of BID schemes and restoration filters have been proposed over the years, ranging from the spatial domain to the frequency domain, parametric to non-parametric. Typical methods include the Richardson-Lucy method, total variation, Wiener filter, maximum likelihood method, minimum entropy deconvolution, recursive inverse filter, simulated annealing, and multi-channel blind deconvolution (Richardson, 1972;Wiggins, 1978;Lagendijk et al, 1988;Kundur and Hatzinakos, 1996;Banham and Katsaggelos, 1997;Chan and Wong, 1998), as well as their recent improvements (Chen and Cheng, 2011;Szolgay and Szirányi, 2011;Wang and Li, 2011;Yang and Liu, 2011). These methods do provide, to some extent, solutions to the BID problem; however, many are not satisfactory in terms of robustness and performance.…”