This work applies sparse representations and nonlinear image processing to two inverse
imaging problems. The first problem involves image restoration, where the aim is to …

The sparsity of signals in a transform domain or dictionary has been exploited in
applications, such as compression, denoising, and inverse problems. More recently, data …

Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving
linear inverse problems is often challenging, with ill-conditioned operators and potentially …

Recent work in image processing suggests that operating on (overlapping) patches in an
image may lead to state-of-the-art results. This has been demonstrated for a variety of …

Image understanding has been playing an increasingly crucial role in several inverse
problems and computer vision. Sparse models form an important component in image …

Sparse optimization in overcomplete frames has been widely applied in recent years to ill-
conditioned inverse problems. In particular, analysis-based sparse optimization consists of …

Sparse representations using learned dictionaries have been successful in several image
processing applications. However, using a single dictionary model in inverse problems may …

The solution of inverse problems is of fundamental interest in medical and astronomical
imaging, geophysics as well as engineering and life sciences. Recent advances were made …

Many challenging image processing tasks can be described by an ill-posed linear inverse
problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all …

Exploiting a priori known structural information lies at the core of many image reconstruction
methods that can be stated as inverse problems. The synthesis model, which assumes that …