The course is a graduate-level treatise of advanced aspects of modern signal and image processing focusing on the following topics:
Principles of one- and n-dimensional digital linear shift-invariant systems: Fourier and Z transforms, amplitude and phase, minimum phase and linear phase systems, group and phase delay.
One-dimensional finite impulse response (FIR) filter design: windows, optimal windows, Kaiser windows, optimality criteria: weighted LS and min-max, linear programming formulation, extensions.
Multi-rate processing of one-dimensional signals: principles, rate conversion, polyphase filters, filter banks, QMF filters, perfect reconstruction conditions, time-frequency analysis, short-time Fourier transform (STFT), wavelet transform.
Wavelet image processing: 2D wavelets, pyramid representation, 2D wavelet transform, image compression and enhancement.
Elements of sparse coding and modeling, compressive sensing, robust PCA.
Interpolation of band-unlimited signals: one- and n-dimensional splines, B-splines, polynomial splines, coefficient computation using linear filters.
Nonlinear filtering: principles, median and order filters, bilateral filter, retinex.