Related papers: Sparse regularization in limited angle tomography
We obtain bounds on estimation error rates for regularization procedures of the form \begin{equation*} \hat f \in {\rm argmin}_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\left(Y_i-f(X_i)\right)^2+\lambda \Psi(f)\right) \end{equation*} when $\Psi$…
We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…
We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Microwave Tomography (MWT) aims to reconstruct the dielectric properties of tissues from measured scattered electromagnetic fields. This inverse problem is highly nonlinear and ill-posed, posing significant challenges for conventional…
In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…
Channel estimation poses significant challenges in millimeter-wave massive multiple-input multiple-output systems, especially when the base station has fewer radio-frequency chains than antennas. To address this challenge, one promising…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…
We present a note on the implementation and efficacy of a box-constrained $L_1/L_2$ regularization in numerical optimization approaches to performing tomographic reconstruction from a single projection view. The constrained $L_1/L_2$…
The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…
In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…
High density implants such as metals often lead to serious artifacts in the reconstructed CT images which hampers the accuracy of image based diagnosis and treatment planning. In this paper, we propose a novel wavelet frame based CT image…
A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus.…
A long-standing challenge in tomography is the 'missing wedge' problem, which arises when the acquisition of projection images within a certain angular range is restricted due to geometrical constraints. This incomplete dataset results in…
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…