A robust variational model for positive image deconvolution. Issue 2 (February 2016)

• Record Type: Journal Article
• Authors: Welk, Martin
• Is Part Of: Signal, image and video processing. Volume 10:Issue 2(2016)
• Page Start: 369
• Page End: 378
• Publication Date: 2016-02
• Subjects: Non-blind deblurring -- Richardson–Lucy deconvolution -- Regularization -- Robust data term; Signal processing -- Digital techniques -- Periodicals; Image processing -- Digital techniques -- Periodicals; Digital video -- Periodicals; 621.3822
• DOI: 10.1007/s11760-015-0750-z
• Languages: English
• ISSNs: 1863-1703

Abstract

Abstract In this paper, an iterative method for robust deconvolution with positivity constraints is discussed. It is based on the known variational interpretation of the Richardson–Lucy iterative deconvolution as fixed-point iteration for the minimisation of an information divergence functional under a multiplicative perturbation model. The asymmetric penaliser function involved in this functional is then modified into a robust penaliser and complemented with a regulariser. The resulting functional gives rise to a fixed-point iteration that we call robust and regularised Richardson–Lucy deconvolution. It achieves an image restoration quality comparable to state-of-the-art robust variational deconvolution with a computational efficiency similar to that of the original Richardson–Lucy method. Experiments on synthetic and real-world image data demonstrate the performance of the proposed method.