There has been a growing interest in the different types of dictionaries that can be used in image processing applications. We propose a hybrid dictionary composed of transform based atoms and additional nonlinear atoms generated using the polynomial, rectangular and exponential functions. The additional nonlinear atoms improve signal reconstruction quality for both transient and smooth signals. To further improve signal reconstruction quality, we optimize the hybrid dictionary using training samples from the signal. We also propose a signal coding algorithm that generates additional atoms by performing a circular shift on the provided dictionary prior to coding the signal.
We have evaluated the proposed methods against existing predefined dictionaries by visually examining the reconstructed images as well as evaluating the peak signal to noise ratio of the reconstructed signal. All methods proposed in this thesis improved signal reconstruction quality however; we require an in-depth cost analysis study to evaluate its limitations.