Optimizing Codes for Source Separation in Color Image Demosaicing and Compressive Video Recovery

TL;DR

This paper develops optimized code patterns for source separation in color image demosaicing and video recovery by minimizing mutual coherence, explicitly considering practical constraints like non-negativity, block structure, and circular shifts.

Contribution

It introduces a method to design code patterns that account for application-specific constraints, improving reconstruction performance in compressed sensing tasks.

Findings

Optimized codes reduce mutual coherence, enhancing separation quality.

Explicitly considering structure improves practical applicability.

Method outperforms traditional random codes in experiments.

Abstract

There exist several applications in image processing (eg: video compressed sensing [Hitomi, Y. et al, "Video from a single coded exposure photograph using a learned overcomplete dictionary"] and color image demosaicing [Moghadam, A. A. et al, "Compressive Framework for Demosaicing of Natural Images"]) which require separation of constituent images given measurements in the form of a coded superposition of those images. Physically practical code patterns in these applications are non-negative, systematically structured, and do not always obey the nice incoherence properties of other patterns such as Gaussian codes, which can adversely affect reconstruction performance. The contribution of this paper is to design code patterns for video compressed sensing and demosaicing by minimizing the mutual coherence of the matrix $\boldsymbol{\Phi \Psi}$ where $\boldsymbol{\Phi}$ represents the sensing matrix created from the code, and $\boldsymbol{\Psi}$ is the signal representation matrix. Our main contribution is that we explicitly take into account the special structure of those code patterns as required by these applications: (1)~non-negativity, (2)~block-diagonal nature, and (3)~circular shifting. In particular, the last property enables for accurate and seamless patch-wise reconstruction for some important compressed sensing architectures.