Related papers: L0TV: A Sparse Optimization Method for Impulse Noi…
We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there…
In this article, we introduce a minimization model via a non-convex transformed $\ell_p$ (TLp) penalty function with two parameters $a\in(0,\infty)$ and $p\in(0,1]$, where the case $p=1$ is known and was established by S. Zhang and J. Xin.…
An efficient nonlinear contrast source inversion scheme for electromagnetic imaging of sparse two-dimensional investigation domains is proposed. To avoid generating a sequence of linear sparse optimization problems, the non-linearity is…
We develop a dictionary learning algorithm by minimizing the $\ell_1$ distortion metric on the data term, which is known to be robust for non-Gaussian noise contamination. The proposed algorithm exploits the idea of iterative minimization…
Investigation of image reconstruction from data collected over a limited angular range in X-ray CT remains a topic of active research because it may yield insight into the development of imaging workflow of practical significance. This…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
While Total Variation (TV) excels in noise reduction and edge preservation, its reliance on a scalar regularization parameter limits adaptivity. In this study, we present a Learnable Total Variation (LTV) framework coupling an unrolled TV…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
We introduce Back to Basics (BTB), a fast iterative algorithm for noise reduction. Our method is computationally efficient, does not require training or ground truth data, and can be applied in the presence of independent noise, as well as…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
This paper proposes a nonlinear weighted anisotropic total variation (NWATV) regularization technique for electrical impedance tomography (EIT). The key idea is to incorporate the internal inhomogeneity information (e.g., edges of the…
This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on the…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
Poisson noise commonly occurs in images captured by photon-limited imaging systems such as in astronomy and medicine. As the distribution of Poisson noise depends on the pixel intensity value, noise levels vary from pixels to pixels. Hence,…
Clipping is one of the simplest peak-to-average power ratio (PAPR) reduction schemes for orthogonal frequency division multiplexing (OFDM). Deliberately clipping the transmission signal degrades system performance, and clipping mitigation…
This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based…
The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide…