Related papers: Revisit 1D Total Variation restoration problem wit…
In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…
We consider $L^1$-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is non-convex for circle-valued data. In this paper,…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
In this paper, we propose Total Variation Regularized Tensor-on-scalar Regression(TVTR), a novel method for estimating the association between a tensor outcome (a one dimensional or multidimensional array) and scalar predictors. While the…
We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an…
Experimentally acquired microscopy images are unavoidably affected by the presence of noise and other unwanted signals, which degrade their quality and might hide relevant features. With the recent increase in image acquisition rate, modern…
We propose an adaptive method for online time-varying (TV) convex optimization, termed $\mathcal{L}_{1}$ adaptive optimization ($\mathcal{L}_{1}$-AO). TV optimizers utilize a prediction model to exploit the temporal structure of TV…
Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating…
Image segmentation with a volume constraint is an important prior for many real applications. In this work, we present a novel volume preserving image segmentation algorithm, which is based on the framework of entropic regularized optimal…
Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…
Denoising is of utmost importance for the visualization and processing of images featuring low signal-to-noise ratio. Total variation methods are among the most popular techniques to perform this task improving the signal-to-noise ratio…
Sampling high-dimensional images is challenging due to limited availability of sensors; scanning is usually necessary in these cases. To mitigate this challenge, snapshot compressive imaging (SCI) was proposed to capture the…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings…
Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang [{\em SIAM J. Imaging Sci.}, 1 (2008), pp. 248--272]. The method in a nutshell consists of a…
The $\ell^1$ and total variation (TV) penalties have been used successfully in many areas, and the combination of the $\ell^1$ and TV penalties can lead to further improved performance. In this work, we investigate the mathematical theory…
Optimization within a layer of a deep-net has emerged as a new direction for deep-net layer design. However, there are two main challenges when applying these layers to computer vision tasks: (a) which optimization problem within a layer is…
Low-rank Deconvolution (LRD) has appeared as a new multi-dimensional representation model that enjoys important efficiency and flexibility properties. In this work we ask ourselves if this analytical model can compete against Deep Learning…
Consider the problem of reconstructing a multidimensional signal from an underdetermined set of measurements, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such…