Tomographic reconstruction by maximum entropy in the mean: Unconstrained reconstructions (Q1855692)

The goal in this paper is to present a new wavelet regularization method for determining the surface heat flux and give out some error estimates. The author provides a multiresolution definition and gives the regularization of such operators with convolutional kernels, which are homogeneous or associated homogeneous functions, and establishes some general results concerning kernels in a multiresolution analysis. Then the author provides concise numerical procedures for the construction and application of singular and hyper-singular operators. The author also comments regarding the use of other bases, especially the compactly supported B-spline. Lastly, the author gives some examples of kernels that can be regularized by the multiresolution procedure, and develops an application, a fast algorithm for evaluation of discrete sums.