In this project, we develop a Hierarchical Decomposition algorithm to solve the `1-Regularized Least Square problem: min x∈Rn {||x||`1 ∣∣Ax = b}. With the new approach, we show a systemic approach on how to select a family of regularization parameters λ’s in order to improve accuracy while retaining the sparsity of our approximation. 1 Background: A Constrained `0 Minimization In the recent dec...

An image registration technique is presented for the registration of medical images using a hybrid combination of coarse-scale landmark and B-splines deformable registration techniques. The technique is particularly effective for registration problems in which the images to be registered contain large localized deformations. A brief overview of landmark and deformable registration techniques is...

Much attention has been paid in the literature to total-variation-diminishing (TVD) numerical processes in the solution of nonlinear hyperbolic differential equations. For special Runge– Kutta methods, conditions on the stepsize were derived that are sufficient for the TVD property; see, e.g., Shu and Osher [J. Comput. Phys., 77 (1988), pp. 439–471] and Gottlieb and Shu [Math. Comp., 67 (1998),...

The entropy condition and the total variation boundedness of weak solutions of convex scalar conservation laws are enforced by Lip+-stability which the physical solutions satisfy. The first order Godunov and LaxFriedrichs schemes, and the second order Maxmod scheme are consistent with this Lip+-stability and are, therefore, entropy convergent. In this paper, a uniformly third order accurate sch...

We discuss the reconstruction of piecewise smooth data from its (pseudo-) spectral information. Spectral projections enjoy superior resolution provided the data is globally smooth, while the presence of jump discontinuities is responsible for spurious O(1) Gibbs oscillations in the neighborhood of edges and an overall deterioration to the unacceptable rst-order convergence rate. The purpose is ...

We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws arising in the simulation of multiphase flows in heterogeneous porous media. We compare the Kurganov-Tadmor (KT) [3] semi-discrete central scheme with the NessyahuTadmor (NT) [27] central scheme. The KT scheme uses more precise information about the local speeds of propagation together with integr...