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

We derive the Fourier Slice Theorem, and breifly discuss the relation to Radar Imaging Problems.

An Introduction to Compressed Sensing

An introduction to theory of compressed sensing, a method for reconstruction of sparse signals from limited data.

Chebyshev's Alternations 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 Whitney'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 tranform.  We derive the classical fourier slice theorem, and give a complete proof showing the reconstruction of a function from its Radon tranform using orthogonal ridge polynomials.