Sparsity constrained image reconstruction using nonlinear dictionary atoms with time-shifted OMP signal coding algorithm

Complex signals such as images, audio and video recordings can be represented by a large over-complete dictionary without significant compromise on the representation quality. An over-complete dictionary has many more columns than the number of rows. Large over-complete dictionaries can produce sparse representation vectors and provide significant improvements in the reconstructed signal quality because it contains many patterns to select from. The use of the over-complete dictionaries and sparse coding has been successfully applied in compression, de-noising, and pattern recognition applications within the last few decades. An example of an over-complete dictionary that has seen a great deal of success in image processing applications is the Discrete Cosine Transform (DCT) dictionary. However, we propose a novel non-linear overcomplete dictionary that improves the quality of the signal representation while reducing the number of non-zero elements to represent the signal. The proposed non-linear dictionary has demonstrated through experimental results to be superior to the DCT dictionary by achieving higher signal to noise ratio (SNR) in the reconstructed images.