Dictionary learning with the cosparse analysis model based on summation of blocked determinants as the sparseness measure |
| |
Affiliation: | 1. Department of Mathematics, University of Texas at Austin, RLM 8.100, 2515 Speedway Stop C1200, Austin, TX 78712-1202, USA;2. Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX 77843–3368, USA;3. Department of Mathematics and Statistics, James Madison University, Roop Hall 305, MSC 1911, Harrisonburg, VA 22807, USA;1. Departamento de Matemáticas, Universidad de Oviedo, E-33203 Gijón, Spain;2. Departamento de Matemática Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain |
| |
Abstract: | Dictionary learning is crucially important for sparse representation of signals. Most existing methods are based on the so called synthesis model, in which the dictionary is column redundant. This paper addresses the dictionary learning and sparse representation with the so-called analysis model. In this model, the analysis dictionary multiplying the signal can lead to a sparse outcome. Though it has been studied in the literature, there is still not an investigation in the context of dictionary learning for nonnegative signal representation, while the algorithms designed for general signal are found not sufficient when applied to the nonnegative signals. In this paper, for a more efficient dictionary learning, we propose a novel cost function that is termed as the summation of blocked determinants measure of sparseness (SBDMS). Based on this measure, a new analysis sparse model is derived, and an iterative sparseness maximization scheme is proposed to solve this model. In the scheme, the analysis sparse representation problem can be cast into row-to-row optimizations with respect to the analysis dictionary, and then the quadratic programming (QP) technique is used to optimize each row. Therefore, we present an algorithm for the dictionary learning and sparse representation for nonnegative signals. Numerical experiments on recovery of analysis dictionary show the effectiveness of the proposed method. |
| |
Keywords: | Sparse representation Analysis dictionary learning Summation of blocked determinants measure of sparseness (SBDMS) Nonnegative Analysis model |
本文献已被 ScienceDirect 等数据库收录! |
|