Learning Scale and Shift-Invariant Dictionary for Sparse Representation

Sparse representation is a signal model to represent signals with a linear combination of a small number of prototype signals called atoms, and a set of atoms is called a dictionary. The design of the dictionary is a fundamental problem for sparse representation. However, when there are scaled or translated features in the signals, unstructured dictionary models cannot extract such features. In this paper, we propose a structured dictionary model which is scale and shift-invariant to extract features which commonly appear in several scales and locations. To achieve both scale and shift invariance, we assume that atoms of a dictionary are generated from vectors called ancestral atoms by scaling and shift operations, and an algorithm to learn these ancestral atoms is proposed.