Fast Deconvolution with Color Constraints on Gradients

In this report, we describe a fast deconvolution approach for color images that combines a sparse regularization cost on the magnitudes of gradients with constraints on their direction in color space. We form these color constraints in a way that allows retaining the computationally-efficient optimization strategy introduced in recent deconvolution methods based on \emph{half-quadratic splitting}. The proposed algorithm is capable of handling a different blur kernel in each color channel, and is used for per-layer deconvolution in our paper: Depth and Deblurring from a Spectrally-varying Depth-of-Field. A MATLAB implementation of this method takes roughly 20 seconds to deconvolve a three-channel 1544x1028 color image, on a Linux-based Intel I-3 2.1GHz machine.