Related papers: Convergence and performances of the peeling wavele…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
In this paper, the problem of de-noising of an image contaminated with additive white Gaussian noise (AWGN) is studied. This subject has been continued to be an open problem in signal processing for more than 50 years. In the present paper,…
Grid peeling is the process of repeatedly removing the convex hull vertices of the grid-points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous…
Image denoising is getting more significance, especially in Computed Tomography (CT), which is an important and most common modality in medical imaging. This is mainly due to that the effectiveness of clinical diagnosis using CT image lies…
This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physics. In a wavelet-Galerkin framework, we formulate learning…
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…
Clustering is a ubiquitous problem in data science and signal processing. In many applications where we observe noisy signals, it is common practice to first denoise the data, perhaps using wavelet denoising, and then to apply a clustering…
Demixing is the problem of identifying multiple structured signals from a superimposed observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. We present a new solution to determine…
We consider the estimation of the regularization parameter for the simultaneous deblurring of multiple noisy images via Tikhonov regularization. We approach the problem in three ways. We first reduce the problem to a single-image deblurring…
We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for…
Image denoising is a classical signal processing problem that has received significant interest within the image processing community during the past two decades. Most of the algorithms for image denoising has focused on the paradigm of…
Both wavelet denoising and denosing methods using the concept of sparsity are based on soft-thresholding. In sparsity based denoising methods, it is assumed that the original signal is sparse in some transform domains such as the wavelet…
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 unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension…
A signature result in compressed sensing is that Gaussian random sampling achieves stable and robust recovery of sparse vectors under optimal conditions on the number of measurements. However, in the context of image reconstruction, it has…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
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…
We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the…
We present a framework for the optimal filtering of spherical signals contaminated by realizations of an additive, zero-mean, uncorrelated and anisotropic noise process on the sphere. Filtering is performed in the wavelet domain given by…
The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet…