Generalized Phi Number System and its Applications for Image Decomposition and Enhancement

Technologies and applications of the field-programmable gate array (FPGAs) and digital signal processing (DSP) require both new customizable number systems and new data formats. This paper introduces a new class of parameterized number systems, namely the generalized Phi number system (GPNS). By selecting appropriate parameters, the new system derives the traditional Phi number system, binary number system, beta encoder, and other commonly used number systems. GPNS also creates new opportunities for developing customized number systems, multimedia security systems, and image decomposition and enhancement systems. A new image enhancement algorithm is also developed by integrating the GPNS-based bit-plane decomposition with Parameterized Logarithmic Image Processing (PLIP) models. Simulation results are given to demonstrate the GPNS's performance.