Sequential minimal eigenvalues - An approach to analysis dictionary learning

Over the past decade there has been a great interest in a synthesis-based model for signals, based on sparse and redundant representations. Such a model assumes that the signal of interest can be decomposed as a linear combination of few columns from a given matrix (the dictionary). An alternative, analysis-based, model can be envisioned, where an analysis operator multiplies the signal, leading to a sparse outcome. In this paper we propose a simple but effective analysis operator learning algorithm, where analysis "atoms" are learned sequentially by identifying directions that are orthogonal to a subset of the training data. We demonstrate the effectiveness of the algorithm in three experiments, treating synthetic data and real images, showing a successful and meaningful recovery of the analysis operator.