Biomedical photoacoustic tomography, which can provide high-resolution 3D soft tissue
images based on optical absorption, has advanced to the stage at which translation from the …

A large number of imaging problems reduce to the optimization of a cost function, with
typical structural properties. The aim of this paper is to describe the state of the art in …

Inverse problems arise from the need to interpret indirect and incomplete measurements. As
an area of contemporary mathematics, the field of inverse problems is strongly driven by …

Denoising is the problem of removing noise from an image. The most commonly studied
case is with additive white Gaussian noise (AWGN), where the observed noisy image f is …

We propose a new definition for the gradient field of a discrete image defined on a twice
finer grid. The differentiation process from an image to its gradient field is viewed as the …

We introduce novel image regularization penalties to overcome the practical problems
associated with the classical total variation (TV) scheme. Motivated by novel …

Estimation of the regularization parameter, which strikes a balance between the data fidelity
and regularity, is essential for successfully solving ill-posed image restoration problems …

Euler's elastica model has a wide range of applications in image processing and computer
vision. However, the nonconvexity, the nonsmoothness, and the nonlinearity of the …

We present and compare various types of discretizations which have been proposed to
approximate the total variation (mostly, of a gray-level image in two dimensions). We discuss …

Abstract Quantitative Magnetic Resonance (MR) imaging provides reproducible
measurements of biophysical parameters, and has become an essential tool in clinical MR …