相关论文: Fractional total variation denoising model with $L…

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000)…

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for $L^1$ regularization of inverse problems…

Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…

We study the regularity of solutions to a nonlocal variational problem, which is related to the image denoising model, and we show that, in two dimensions, minimizers have the same H\"older regularity as the original image. More precisely,…

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…

Reconstructing images from ill-posed inverse problems often utilizes total variation regularization in order to recover discontinuities in the data while also removing noise and other artifacts. Total variation regularization has been…

We consider the problem of image denoising in the presence of noise whose statistical properties are a combination of two different distributions. We focus on noise distributions that are frequently considered in applications, in particular…

Using total variation based energy minimisation we address the recovery of a blurred (convoluted) one dimensional (1D) barcode. We consider functionals defined over all possible barcodes with fidelity to a convoluted signal of a barcode,…

This work addresses a central topic in Magnetic Resonance Imaging (MRI) which is the motion-correction problem in a joint reconstruction and registration framework. From a set of multiple MR acquisitions corrupted by motion, we aim at -…

In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation…

Bias in image restoration algorithms can hamper further analysis, typically when the intensities have a physical meaning of interest, e.g., in medical imaging. We propose to suppress a part of the bias -- the method bias -- while leaving…

In this paper, we propose a new variational framework for 3D surface denoising over triangulated meshes, which is inspired by the success of semi-sparse regularization in image processing. Differing from the uniformly sampled image data,…

We prove regularity results for the unique minimizer of the total variation functional, currently used in image processing analysis since the work by L. Rudin, S. Osher and E. Fatemi. In particular we show that if the source term $f$ is…

Let $u \in \mbox{BV}(\Omega)$ solve the total variation denoising problem with $L^2$-squared fidelity and data $f$. Caselles et al. [Multiscale Model. Simul. 6 (2008), 879--894] have shown the containment $\mathcal{H}^{m-1}(J_u \setminus…

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…

Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double…

In this paper we analyse an infimal convolution type regularisation functional called $\mathrm{TVL}^{\infty}$, based on the total variation ($\mathrm{TV}$) and the $\mathrm{L}^{\infty}$ norm of the gradient. The functional belongs to a more…

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 study the problem of deconvolution for light-sheet microscopy, where the data is corrupted by spatially varying blur and a combination of Poisson and Gaussian noise. The spatial variation of the point spread function (PSF) of a…