Related papers: Total Variation Denoising via the Moreau Envelope
The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…
Tensor completion is a technique of filling missing elements of the incomplete data tensors. It being actively studied based on the convex optimization scheme such as nuclear-norm minimization. When given data tensors include some noises,…
The L1 norm regularized least squares method is often used for finding sparse approximate solutions and is widely used in 1-D signal restoration. Basis pursuit denoising (BPD) performs noise reduction in this way. However, the shortcoming…
We revisit the recently proposed ``self-Wiener" (SW) filtering method for robust deconvolution, and generalize it to the classical denoising problem. The resulting estimator, termed generalized SW (GSW) filtering, retains the nonlinear…
This paper introduces a novel ridgelet transform-based method for Poisson image denoising. Our work focuses on harnessing the Poisson noise's unique non-additive and signal-dependent properties, distinguishing it from Gaussian noise. The…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a…
Noise is a major issue while transferring images through all kinds of electronic communication. One of the most common noise in electronic communication is an impulse noise which is caused by unstable voltage. In this paper, the comparison…
1D Total Variation (TV) denoising, considering the data fidelity and the Total Variation (TV) regularization, proposes a good restored signal preserving shape edges. The main issue is how to choose the weight $\lambda$ balancing those two…
We consider the problem of estimating a function defined over $n$ locations on a $d$-dimensional grid (having all side lengths equal to $n^{1/d}$). When the function is constrained to have discrete total variation bounded by $C_n$, we…
The measurements of very low level signals at low frequency is a very difficult problem, because environmental noise increases in this frequency domain and it is very difficult to filter it efficiently. In order to counteract these major…
We consider the problem of robust deconvolution, and particularly the recovery of an unknown deterministic signal convolved with a known filter and corrupted by additive noise. We present a novel, non-iterative data-driven approach.…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
We propose a hybrid method combining partial differential equation (PDE) and Monte Carlo (MC) techniques to obtain efficient estimates of statistics for plastic deformation related to kinematic hardening models driven by transient coloured…
Convolutional neural networks (CNNs) have shown outstanding performance on image denoising with the help of large-scale datasets. Earlier methods naively trained a single CNN with many pairs of clean-noisy images. However, the conditional…
We introduce a new analysis method to deal with stationary non-Gaussian noises in gravitational wave detectors in terms of the independent component analysis. First, we consider the simplest case where the detector outputs are linear…
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
A new thresholding strategy for the estimation of a deterministic image immersed in noise is introduced. The threshold is combined with a wavelet decomposition, where the wavelet coefficient of the image at any fixed value of the…
In this paper, the traditional model based variational method and learning based algorithms are naturally integrated to address mixed noise removal problem. To be different from single type noise (e.g. Gaussian) removal, it is a challenge…