Adaptive complex-valued dictionary learning: Application to fMRI data analysis

Abstract

Complex-valued signals arise naturally in a wide-range of applications such as radar, magnetic resonance imaging (MRI), functional MRI (fMRI), remote sensing, communication systems, etc. In this article, we propose an adaptive dictionary learning (DL) algorithm for such complex-valued signals. The algorithm is derived via adaptively penalized, sequential rank-1 matrix approximations using the ℓ1-norm as sparsity inducing penalty. Instead of alternating between sparse coding and dictionary update stages, each atom and its support are updated alternately with both variables admitting simple closed form solutions. A comprehensive performance comparison on simulated as well as experimental task-..