**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