Harmonic Analysis for Signal Processing, Spring 2011 Harmonic Analysis for Signal Processing, Spring 2011, Notes

Harmonic Analysis for Signal Processing, Spring 2011, Notes

I. Orthobases and Frames

Notes 01, norms, inner products, orthobases, and projections

 

 

 

Notes 02, non-orthgonal bases (Riesz bases)

Notes 03, frames
Notes 04, additional notes on frame operators (updated 1/28; fixed some minor typos)

II. Time-frequency bases and frames
Notes 05, windowed Fourier systems
Notes 06, lapped orthogonal transforms
Notes 07, best basis and CART
Notes 08, wavelets and multiresolution approximations
Notes 09, Daubechies wavelets
Notes 10, filterbanks, biorthogonal wavelets, and wavelets in 2D

III. Approximation theory
Notes 11, introduction to approximation theory

IV. Denoising and linear Inverse problems
Notes 12, nonlinear estimation by hard- and soft-thresholding
Notes 13, linear inverse problem and the wavelet-vaguelette decomposition

Interlude: Notes 14, introduction to curvelets

V.  Compressive sensing
Notes 15, finding sparse decompositions in unions of orthobases using basis pursuit
Notes 16, undetermined systems and the restricted isometry property
Notes 17, recovery via l1 minimization