Multichannel blind iterative image restoration

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Abstract
Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately, in a single-channel framework, serious conceptual and numerical problems are often encountered. An eigenvector-based method (EVAM) has been proposed for a multichannel framework which determines perfectly convolution masks in a noise-free environment if channel disparity, called co-primeness, is satisfied (see Harikumar, G. and Bresler, Y., ibid., vol.8, no.2, p.202-19, 1999; Proc. ICIP 96, vol.3, p.97-100, 1996). We propose a novel iterative algorithm based on recent anisotropic denoising techniques of total variation and a Mumford-Shah functional with the EVAM restoration condition included. A linearization scheme of half-quadratic regularization together with a cell-centered finite difference discretization scheme is used in the algorithm and provides a unified approach to the solution of total variation or Mumford-Shah. The algorithm performs well even on very noisy images and does not require an exact estimation of mask orders. We demonstrate the capabilities of the algorithm on synthetic data. Finally, the algorithm is applied to defocused images taken with a digital camera and to data from astronomical ground-based observations of the Sun.

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