# Toby Sanders, Ph.D.

# Senior Research Scientist @

# Lickenbrock Technologies, INC

# Saint Louis, MO

# company website

##### 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.