Sequential Minimal Eigenvalues - An Approach to Analysis Dictionary Learning

Abstract

International audienceOver the past decade there has been a great interest in asynthesis-based model for signals, based on sparse and re-dundant representations. Such a model assumes that the sig-nal of interest can be decomposed as a linear combinationof few columns from a given matrix (the dictionary). An al-ternative, analysis-based, model can be envisioned, where ananalysis operator multiplies the signal, leading to a sparseoutcome. In this paper we propose a simple but effectiveanalysis operator learning algorithm, where analysis "atoms"are learned sequentially by identifying directions that are or-thogonal to a subset of the training data. We demonstratethe effectiveness of the algorithm in three experiments, treat-ing synthetic data and real images, showing a successful andmeaningful recovery of the analysis operator