Dictionaries for Sparse Representation Modeling Digital sampling can display signals, and it should be possible to expose a large part of the desired signal information with only a limited signal sample.
Ron Rubinstein, Alfred Marcel Bruckstein, Michael Elad · 2010
Sparse and redundant representation modeling of data assumes an ability to describe signals as linear combina- tions of a few atoms from a pre-specified dictionary. As such, the choice of the dictionary that sparsifies the signals is crucial for the success of this model. In general, the choice of a proper dictionary can be done using one of two ways: i) building a sparsifying dictionary based on a mathematical model of the data, or ii) learning a dictionary to perform best on a training set. In this paper we describe the evolution of these two paradigms. As manifestations of the first approach, we cover topics such as wavelets, wavelet packets, contourlets, and curvelets,allaimingtoexploit1-Dand2-Dmathematicalmodels for constructing effective dictionaries for signals and images. Dictionary learning takes a different route, attaching the dictionary to a set of examples it is supposed to serve. From the seminal work of Field and Olshausen, through the MOD, the K-SVD, the Generalized PCA and others, this paper surveys the various options such training has to offer, up to the most recent contributions and structures.