Alternating Direction Method of Multipliers for Solving Dictionary Learning Models

Sparse representations and coupled dictionary learning for the enhancement of computational imaging systems

“…In chapter 5, we present our main theoretical contribution of this dissertation. Specifically, we propose a novel Coupled Dictionary Learning scheme, based on the efficient scheme of the Alternating Direction Method of Multipliers (ADMM) [29,141]. Additionally, we provide the entire theoretical study, including the mathematical proof.…”

“…(10.2), we exploit the scheme of the Alternating Direction Method of Multipliers (ADMM) [29]. Taking into consideration the very good performance of ADMM in several inverse image processing problems [141], it is a natural choice to utilize for the proposed blind image de-convolution scheme. Reformulating (10.2) in a suitable form for the ADMM by introducing auxiliary variables, along with their constraints, the minimization problem is given by:…”

“…We propose a computationally efficient coupled dictionary learning technique, based on the Alternating Direction Method of Multipliers ADMM [29,101,111,141] formulation, that converts the constrained dictionary learning problem posed in (5.4), into an unconstrained version which can be efficiently solved via alternating minimizations. Formally, we consider the observation, and the latent feature spaces, as: S X {s X } N i 1 and S Z {s Z } P i 1 .…”