A new efficient dictionary and its implementation on retinal images

Sparse representation of signals and images using an over-complete basis function (dictionary) has attracted a lot of attention in the literature recently. Atoms of a dictionary are either chosen from a predefined set of functions (e.g. Sine, Cosine or Wavelets), or learned from a training set (KSVD). Recently, a nonlinear (NL) dictionary has been proposed by adding NL functions, such as polynomials, rational, logarithmic, exponential, and phase shifted and higher order cosine functions to the conventional Discrete Cosine Transform (DCT) atoms. In this paper, we present a comprehensive performance comparison of various NL functions that are added to the DCT dictionary. The NL dictionary is also compared with the other known dictionaries such as DCT, Haar and KSVD-based learned dictionary for sparse image reconstruction. In the second part, the NL dictionary is exploited for sparsity based image denoising. Retinal images are used for the analysis.