Sequential Minimal Eigenvalues - An Approach to Analysis Dictionary Learning

Boaz Ophir (1) , Michael Elad (1) , Nancy Bertin (2) , Mark D. Plumbley (3)

1 Department of Computer Science [Haifa]
2 METISS - Speech and sound data modeling and processing
3 Centre for Digital Music

Over 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.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Boaz Ophir, Michael Elad, Nancy Bertin, Mark D. Plumbley. Sequential Minimal Eigenvalues - An Approach to Analysis Dictionary Learning. The 19th European Signal Processing Conference (EUSIPCO‐2011), Aug 2011, Barcelona, Spain. ⟨inria-00577231⟩