Notes on automated parameter selection for regularization methods in signal and image reconstruction 

A terse introduction to parameter selection for regularization in image reconstruction.

Radon Transform, Projections, Fourier Slice Theorem, Backprojection Methods, and Relationship to Radar Imaging

The Fourier Slice Theorem is derived, and briefly discuss the relation to radar imaging problems.

An Introduction to Compressed Sensing

A method for reconstruction of sparse signals from limited samples.

Chebyshev's Alternating Theorem

A detailed proof of Chebyshev's alternation theorem, about the best degree n polynomial of best uniform approximation to continuous functions.

Whitney's Theorem

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.

Radon Transform

An introduction to the Radon transform and reconstruction of a function from its Radon transform using orthogonal ridge polynomials.