We formulate a solution to the diffuse optical tomography (DOT) inverse problem as the minimization of an energy functional of the solution and the data. For the solution prior we introduce a local diffusion regularization potential with a threshold based on robust statistics (the Hubert function). We compare results on simulated data for the Hubert function and two other standard regularizatio...

The generalized singular value decomposition (GSVD) often is used to solve Tikhonov regularization problems with a regularization matrix without exploitable structure. This paper describes how the standard methods for the computation of the GSVD of a matrix pair can be simplified in the context of Tikhonov regularization. Also, other regularization methods, including truncated GSVD, are conside...

One of the essential ways in which nonlinear image restoration algorithms differ from linear, convolution-type image restoration filters is their capability to restrict the restoration result to nonnegative intensities. The iterative constrained Tikhonov-Miller (ICTM) algorithm, for example, incorporates the nonnegativity constraint by clipping all negative values to zero after each iteration. ...

We describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the dissipation of cardiac wave fronts and the shape...

The problem of convergence of a special form of the generalized pulsespectrum technique (GPST) for solving inverse problems of one-dimensional diffusion equations in space-time domain is considered. Under the assumptions that a Tikhonov regularized solution exists and the derivative operator of the regularized forward problem at the regularized solution is invertible, the iterative solutions of...

bstract. In this paper, a multiple description image coding cheme is proposed to facilitate the transmission of images over edia with possible packet loss. The proposed method is based on nding the optimal reconstruction filter coefficients that will be used o reconstruct lost descriptions. For this purpose initially, the original mage is downsampled and each subimage is coded using standard PE...