Notes on automated parameter selection for regularization methods in signal and image reconstruction
A terse introduction to parameter selection for regularization in image reconstruction.
The Fourier Slice Theorem is derived, and briefly discuss the relation to radar imaging problems.
A method for reconstruction of sparse signals from limited samples.
A detailed proof of Chebyshev's alternation theorem, about the best degree n polynomial of best uniform approximation to continuous functions.
A detailed proof of Witney's Theorem from 1957, giving an upper bound on the rate of approximation of the space L_p[a,b] from polynomials. The upper bound is given through the modulus of smoothness. Included is the special case of 0<p<1.
An introduction to the Radon transform and reconstruction of a function from its Radon transform using orthogonal ridge polynomials.