Beta wavelets. Synthesis and application to lossy image compression

Wavelets are known to have many connections to several other parts of mathematics, notably phase-space analysis of signal processing, reproducing kernel Hilbert spaces, coherent states in quantum mechanics, spline approximation theory, windowed Fourier transforms, filter banks and image analysis. In this paper, we study a new orthogonal mother wavelet and wavelet basis system based on Beta function as well as its derivatives. The most important conditions of mother wavelets to be satisfied are the admissibility, the regularity and the orthogonality. All these conditions were verified in the case of the proposed Beta wavelets family. Compared to most known wavelets as Haar, Daubechies, and Coifflet ones, the Beta wavelet family improves efficient results and performances presented in this paper for image compression context.