Related papers: Image Denoising Using Transformed L1 (TL1) Regular…
In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger…
The Retinex theory models the image as a product of illumination and reflection components, which has received extensive attention and is widely used in image enhancement, segmentation and color restoration. However, it has been rarely used…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
Plug-and-Play optimization recently emerged as a powerful technique for solving inverse problems by plugging a denoiser into a classical optimization algorithm. The denoiser accounts for the regularization and therefore implicitly…
This work addresses the recovery and demixing problem of signals that are sparse in some general dictionary. Involved applications include source separation, image inpainting, super-resolution, and restoration of signals corrupted by…
Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency…
Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging…
This article proposes a novel regularization method, named Geometric Spatio-Spectral Total Variation (GeoSSTV), for hyperspectral (HS) image denoising and destriping. HS images are inevitably affected by various types of noise due to the…
We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve $L_1$/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
We propose a PDE-constrained optimization approach for the determination of noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise…
As graph data collected from the real world is merely noise-free, a practical representation of graphs should be robust to noise. Existing research usually focuses on feature smoothing but leaves the geometric structure untouched.…
We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L$_2$ and L$_1$ fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer,…
Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure…
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An…