A primal-dual algorithm for joint demosaicking and deconvolution

Abstract

In this paper, we present a first-order primal-dual algorithm for tackling the joint demosaicking and deconvolution problem. The proposed algorithm exploits the sparsity of both discrete gradient (TV) and shearlet coefficients as prior knowledge. In order to deal with this sparsity across the color channels, we first decorrelate the signals in color space before sparsifying them spatially, resulting in a separable transform. We demonstrate that this approach yields better results than employing group sparsity strategies. We propose to update the decorrelation operator during the image reconstruction, this approach will result in a significant improvement in PSNR. By relaxing the sparsity of the chrominance signals, we obtain both better objective and subjective image quality compared to other stateof-the-art demosaicking and deconvolution algorithms. Also, color artifacts due to demosaicking are suppressed very well.

Cross‐channel regularisation for joint demosaicking and intrinsic lens deblurring

“…Fig. 12 Demosaicking-deblurring result on real images using the methods of Condat [27], Menon and Calvagno [20], Kiku et al [6], Luong et al [38], ours…”

“…We also made a comparison with the other three demosaicking methods, and a method that accounts for the lens PSFs in the demosaicking process [38]. In order to provide a fair comparison, for the demosaicking methods that do not explicitly handle lens blur, we performed a post-processing deconvolution, given the lens PSFs.…”

Optimal Algorithms for <formula formulatype="inline"> <tex Notation="TeX">$L_{1}$</tex></formula>-subspace Signal Processing

“…To prove Proposition 3, we will prove that can be computed with complexity . We begin our developments by defining (20) Then, also has rank and can be decomposed by (21) where , , , are the eigenvalue-weighted eigenvectors of with nonzero eigenvalue. By (11),…”

Optimal Algorithms for $L_1$-subspace Signal Processing

“…To prove Proposition 5, it suffices to prove that B opt can be computed with complexity O N rank(X)K−K+1 . As in (20), (21), let d denote the rank of X and QQ T where Q ∈ Ê N ×d is the eigen-decomposition matrix of X T X.…”