Related papers: Total Variation Denoising via the Moreau Envelope
Denoising has always been theoretically considered as removal of high frequency disturbances having Gaussian distribution. Here we relax this assumption and the method used here is completely different from traditional thresholding schemes.…
Removing noise from piecewise constant (PWC) signals, is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need separating into stratigraphic zones,…
This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising…
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…
We present the continuous wavelet transform (WT) of white Gaussian noise and establish a connection to the theory of Gaussian analytic functions. Based on this connection, we propose a methodology that detects components of a signal in…
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…
We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…
The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…
We introduce a new approach for Gaussianity testing using the envelope of a signal and its coefficient of variation. The envelope of a Gaussian signal follows the Rayleigh distribution, and given that the coefficient of variation of the…
In the paper, a new method of blind estimation of noise variance in a single highly textured image is proposed. An input image is divided into 8x8 blocks and discrete cosine transform (DCT) is performed for each block. A part of 64 DCT…
In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed. Compared to the classical nonlocal total variation methods, our method modifies the energy functional to introduce a weight to balance between the labeled…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…
We study a nonlocal version of the total variation-based model with $L^1-$fidelity for image denoising, where the regularizing term is replaced with the fractional $s$-total variation. We discuss regularity of the level sets and uniqueness…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…
In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and some candidate image on a large collection of subboxes. The…
In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is two-fold. Firstly, we formulate the restoration…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
We propose a fully-convolutional neural-network architecture for image denoising which is simple yet powerful. Its structure allows to exploit the gradual nature of the denoising process, in which shallow layers handle local noise…
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…
Total variation has proved its effectiveness in solving inverse problems for compressive sensing. Besides, the nonlocal means filter used as regularization preserves texture better for recovered images, but it is quite complex to implement.…