ECE 6250, Fall 2015 ECE 6250, Fall 2015, Course Notes

ECE 6250, Fall 2015, Course Notes


I. Signal representations in vector spaces
Notes 1, the Shannon-Nyquist sampling theorem
Notes 2, introduction to basis expansions
Notes 3, linear signal spaces
Notes 4, norms and inner products
Notes 5, linear approximation in Hilbert spaces
Notes 6, orthobases
Notes 7, Parseval theorem and Gram-Schmidt
Notes 8, the cosine-I basis, DCT, and JPEG
Notes 9, the lapped orthogonal transform
Notes 10, Haar wavelets
Notes 11, orthonormal wavelets
Notes 12, non-orthogonal bases
Notes 13, splinesII. Linear inverse problems and least-squares signal processing
Notes 14, discretizing inverse problems using bases
Notes 15, solving symmetric systems of equations
Notes 16, the SVD, the least-squares problem, and the pseudo-inverse
Notes 17, stable reconstruction, Tikhonov regularization
Notes 18, weighted least-squares, best linear unbiased estimators

III. Computing the solution to least-squares problems
Notes 19, matrix factorizations, structured matrices
Notes 20, Toeplitz matrices
Notes 21, steepest descent and conjugate gradients
see also An Intro to CG without the agonizing pain
   Notes 22, streaming reconstruction with recursive least-squares
Notes 23, the Kalman filter
Notes 24, adaptive filtering

IV. Matrix approximation using Least-squares
Notes 25, low rank approximation, total least squares, PCA

V. Beyond Least-Squares
Notes 26, norm approximation problems
Notes 27, structured recovery
See also these two review papers: Rev1, Rev2