Regularized Interpolation Driven by Total Variation

Geometry of total variation regularized Lp-model

Nonlinear Interpolation and Total Variation Diminishing Schemes

The Van Leer approach for the approximation of nonlinear scalar conservation laws is studied in one space dimension. The problem can be reduced to a nonlinear interpolation and we propose a convexity property for the interpolated values. We prove that under general hypotheses the method of lines in well posed in l ∩ BV and we give precise sufficient conditions to establish that the total variat...

A Computational Framework for Total Variation-Regularized Positron Emission Tomography

In positron emission tomography, image data corresponds to measurements of emitted photons from a radioactive tracer in the subject. Such count data is typically modeled using a Poisson random variable, leading to the use of the negative-log Poisson likelihood fit-to-data function. Regularization is needed, however, in order to guarantee reconstructions with minimal artifacts. Given that tracer...

The Total Variation Regularized L1 Model for Multiscale Decomposition

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,...

An algorithm for total variation regularized photoacoustic imaging

An algorithm for total variation regularized photoacoustic imaging.