Abstract
In this study, we propose using the least squares optimal deformable filtering approximation as an efficient tool for linear shift variant (SV) filtering, in the context of restoring SV-degraded images. Based on this technique we propose a new formalism for linear SV operators, from which an efficient way to implement the transposed SV-filtering is derived. We also provide a method for implementing an approximation of the regularized inversion of a SV-matrix, under the assumption of having smoothly spatially varying kernels, and enough regularization. Finally, we applied these techniques to implement a SV-version of a recent successful sparsity-based image deconvolution method. A high performance (high speed, high visual quality and low mean squared error, MSE) is demonstrated through several simulation experiments (one of them based on the Hubble telescope PSFs), by comparison to two state-of-the-art methods.
Highlights
For many real imaging devices, especially those designed to be wide-angle, small, cheap and/or extra robust, it may still be reasonable to consider their degradation model as linear, but they may significantly depart from shiftinvariance (SI)
Note that the emphasis in this article is not in the estimation procedure and its associated statistical model, but rather in a set of efficient solutions for adapting a restoration method assuming a linear degradation plus noise, to a shift variant (SV)-scenario.a We demonstrate a high performance through several simulation experiments, comparing to two reference methods
Execution times and main memory requirements are notably higher in BLUR3 than in the other degradation cases in our method. This is due to the fact that the expression HTy in step 4 must be explicitly calculated as a sparse matrix-vector multiplication, because Hubble point spread function (PSF) are not so spectrally concentrated as BLUR1 and BLUR2
Summary
For many real imaging devices, especially those designed to be wide-angle, small, cheap and/or extra robust (for instance, because of having very simple optics), it may still be reasonable to consider their degradation model as linear, but they may significantly depart from shiftinvariance (SI). We chose a state-of-the-art, non-linear, image restoration generic method with a high speed potential, named L0-AbS [22] for testing them, which is applicable to any kind of linear blur (SI or not), and which assumes presence of additive white Gaussian noise. Note that the emphasis in this article is not in the estimation procedure and its associated statistical model (the interested reader is referred to the original study [22], which has been improved and extended in [23,24]), but rather in a set of efficient solutions for adapting a (generic) restoration method assuming a linear degradation plus noise, to a SV-scenario.a We demonstrate a high performance (high speed, high visual quality, low MSE) through several simulation experiments (one of them using the Hubble telescope’s PSFs), comparing to two reference methods.
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