Patch Ordering as a Regularization for Inverse Problems in Image Processing

Patch Ordering as a Regularization for Inverse Problems in Image Processing

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 problems including denoising, inpainting, deblurring, and super-resolution. The work reported in [1, 2] takes an extra step forward by showing that ordering these patches to form an approximate shortest path can be leverag...

Inverse Problems in Image Processing

Inverse problems involve estimating parameters or data from inadequate observations; the observations are often noisy and contain incomplete information about the target parameter or data due to physical limitations of the measurement devices. Consequently, solutions to inverse problems are non-unique. To pin down a solution, we must exploit the underlying structure of the desired solution set....

Adaptive Regularization of Some Inverse Problems in Image Analysis

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the iterative optimization, so that regularization is strongest initially, and wanes as data fidelity improves, with the weight of the regularizer being minimized...

Regularization and Inverse Problems

An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other deconvolution methods are also discussed within the Bayesian context, focusing mainly on the comparison of Wiener filtering, Massive Inference and the Pixon meth...

Sparsity regularization in inverse problems