Related papers: Automated Parameter Selection for Total Variation …
Vision foundation models (VFMs) have demonstrated remarkable capabilities in learning universal visual representations. However, adapting these models to downstream tasks conventionally requires parameter updates, with even…
Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…
We consider the problem of reconstructing 2D images from randomly under-sampled confocal microscopy samples. The well known and widely celebrated total variation regularization, which is the L1 norm of derivatives, turns out to be…
The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…
Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised…
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov…
We introduce a first order Total Variation type regulariser that decomposes a function into a part with a given Lipschitz constant (which is also allowed to vary spatially) and a jump part. The kernel of this regulariser contains all…
We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter $\lambda$ multiple of the $\ell_0$ norm composed…
We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the fidelity weight and weights within the kernel of the nonlocal operator. In both cases we…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to…
In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…
We analyse a variational regularisation problem for mixed noise removal that was recently proposed in [14]. The data discrepancy term of the model combines $L^1$ and $L^2$ terms in an infimal convolution fashion and it is appropriate for…
This review discusses methods for learning parameters for image reconstruction problems using bilevel formulations. Image reconstruction typically involves optimizing a cost function to recover a vector of unknown variables that agrees with…
Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a…
The total variation filtering technique emerges as a highly effective strategy for restoring signals with discontinuities in various parts of their structure. This study presents and implements a one-dimensional signal filtering algorithm…
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…