Wavelets are localized and oscillatory functions that generate bases for several function spaces. The multiresolution framework, meant for constructing wavelets, possesses attractive numerical properties for executing the wavelet decomposition of a function. The course aims at discussing orthogonal/non-orthogonal wavelet bases constructed for the space of square integrable functions. It then discusses the algorithmic as well as the application of discrete wavelets.

Syllabus:

Review of normed linear spaces and Fourier transform, Continuous wavelet transform and its inversion, Discrete wavelets, Frames and Riesz bases, Multiresolution analysis, Splines, Construction of orthonormal wavelets, Decomposition and reconstruction algorithms, Nonorthogonal wavelets, 2D wavelets and applications in image analysis. 

Pre-requisite:  Basic functional analysis