A nonlinear dictionary for image reconstruction

Complex signals such as images, audio and video recordings can be represented by a large over complete dictionary without distinguishable compromise on the representation quality. Large over complete dictionaries with more patterns can be used to increase the sparse coding as well as provide significant improvements in signal representation quality. 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. One particular dictionary, the Discrete Cosine Transform (DCT) dictionary has seen a great deal of success in image processing applications. However, we propose a novel non-linear over-complete dictionary that is sparser than the DCT dictionary while improving the quality of the signal representation. 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.