Dual-energy X-ray tomography is considered in a context where the target under imaging consists of two distinct materials. The materials are assumed to be possibly intertwined space, but at any given location there only one material present. Further, energies chosen so that clear difference spectral dependence attenuation coefficients A novel regularizer presented for inverse problem reconstruc...

In previous work by Rueter et al., low frequency (10–750 kHz) ultrasound was shown to penetrate the lung, motivating its use as a nonionizing tomographic technique for pulmonary monitoring. Here, we present method regularized full waveform inversion low-frequency data. A novel structural similarity index metric (SSIM)-based regularization term is introduced that compares correlation of current ...

We propose a novel formulation to find representatives in data samples via learning with structured sparsity. To find representatives with both diversity and representativeness, we formulate the problem as a structurally-regularized learning where the objective function consists of a reconstruction error and three structured regularizers: (1) group sparsity regularizer, (2) diversity regularize...

Abstract: Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is critical to the interpretability of a learned model. Much of the current literature assumes that covariates are only mildly correlated. However, in mo...

We consider concave continuous-kernel games characterized by monotonicity properties and propose discounted mirror descent type dynamics. introduce two classes of dynamics whereby the associated map is constructed based on a strongly convex or Legendre regularizer. Depending regularizer, we show that these new can converge asymptotically in with merely monotone (negative) pseudogradient. Furthe...

A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A method for constructing regularizers in the new sense is proposed and justified.

We prove that isentropic gas flow does not admit non-degenerate TVD fields on any invariant set M(r0, s0) = {r0 < r < s < s0}, where r, s are Riemann coordinates. A TVD field refers to a scalar field whose spatial variation VarX(φ(τ(t,X), u(t,X))) is nonincreasing in time along entropic solutions. The result is established under the assumption that the Riemann problem defined by an overtaking s...

The one–dimensional differential equations for the conservation mixture mass and mixture momentum coupled by a relative velocity conservation equation have been solved for an isentropic mixture of gas and liquid two–phase flow. Under certain restrictions the resulting system of partial differential equations is hyperbolic and allow discontinuous solutions. These equations have been solved by th...

This paper studies the total variation regularization with an L1 fidelity term (TV-L1) model for decomposing an image into features of different scales. We first show that the images produced by this model can be formed from the minimizers of a sequence of decoupled geometry subproblems. Using this result we show that the TV-L1 model is able to separate image features according to their scales,...

In this paper, we consider convergence of classical high order Godunov-type schemes towards entropy solutions for scalar conservation laws. It is well known that sufficient conditions for such convergence include total variation boundedness of the reconstruction and cell or wavewise entropy inequalities. We prove that under large time steps, we only need total variation boundedness of the recon...