The Convex Relaxation Method on Deconvolution Model withMultiplicative Noise

Abstract

Abstract. In this paper, we consider variational approaches to handle the multiplicative noise removal and deblurring problem. Based on rather reasonable physical blurring-noisy assumptions, we derive a new variational model for this issue. After the study of the basic properties, we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model. The relaxed model is solved by an alternating minimization approach. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.

Two-Step Approach for the Restoration of Images Corrupted by Multiplicative Noise

“…", 7,2)) and a multiplicative noise with variance 0.03, 0.05, and 0.1, respectively; second column: the restored image by the RLO algorithm in [43]; third column: the restored image by the AA algorithm in [1]; fourth column: the restored image by the HNZ algorithm in [36]; fifth column: the restored image by the proposed two-step approach. [43]; third column: the restored image by the AA algorithm in [1]; fourth column: the restored image by the HNZ algorithm in [36]; fifth column: the restored image by the proposed two-step approach. The recovered PSNRs and the computing times of the five methods are shown in Table 5.1, where the best recovered results are shown in boldface.…”

“…7)) and a multiplicative noise with variance 0.03, 0.05, and 0.1, respectively; second column: the restored image by the RLO algorithm in [43]; third column: the restored image by the AA algorithm in [1]; fourth column: the restored image by the HNZ algorithm in [36]; fifth column: the restored image by the proposed two-step approach. ", 7,2)) and a multiplicative noise with variance 0.03, 0.05, and 0.1, respectively; second column: the restored image by the RLO algorithm in [43]; third column: the restored image by the AA algorithm in [1]; fourth column: the restored image by the HNZ algorithm in [36]; fifth column: the restored image by the proposed two-step approach. [43]; third column: the restored image by the AA algorithm in [1]; fourth column: the restored image by the HNZ algorithm in [36]; fifth column: the restored image by the proposed two-step approach.…”

“…The experimental results were compared with some other methods proposed recently for multiplicative noise and blurring removal, including the "RLO" method [43], the "AA" method [1], and the "HNZ" method [36]. For the RLO and AA methods, the number of iterations was set at 1000 to obtain good restoration results.…”

HYPERDIRE HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Horn-type hypergeometric functions of two variables

“…Purely numerical approaches [33] can be applied to for arbitrary values of the parameters. However this technique typically does not produce stable numerical result around region of singularities of hypergeometric function.…”

A Dictionary Learning Approach for Poisson Image Deblurring

“…Multiplicative noise appears in several applications, such as laser imaging, ultrasound imaging, and synthetic aperture radar (SAR) [55]- [59]. In these cases, the image formation process (including blur) can be written…”