Modular ADMM-Based Strategies for Optimized Compression, Restoration, and Distributed Representations of Visual Data

Iterative techniques are a well-established tool in modern imaging sciences, allowing to address complex optimization problems via sequences of simpler computational processes. This approach has been significantly expanded in recent years by iterative designs where explicit solutions of optimization subproblems were replaced by black-box applications of ready-to-use modules for denoising or compression. These modular designs are conceptually simple, yet often achieve impressive results. In this chapter, we overview the concept of modular optimization for imaging problems by focusing on structures induced by the alternating direction method of multipliers (ADMM) technique and their applications to intricate restoration and compression problems. We start by emphasizing general guidelines independent of the module type used and only then derive ADMM-based structures relying on denoising and compression methods. The wide perspective on the topic should motivate extensions of the types of problems addressed and the kinds of black boxes utilized by the modular optimization. As an example for a promising research avenue, we present our recent framework employing black-box modules for distributed representations of visual data.