Related papers: 3-D Projected $ L_{1}$ inversion of gravity data
We describe a parallel iterative least squares solver named \texttt{LSRN} that is based on random normal projection. \texttt{LSRN} computes the min-length solution to $\min_{x \in \mathbb{R}^n} \|A x - b\|_2$, where $A \in \mathbb{R}^{m…
We investigate the practical implementation of Taylor's (2002) 3-dimensional gravitational potential reconstruction method using weak gravitational lensing, together with the requisite reconstruction of the lensing potential. This…
Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical…
We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…
We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…
We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a…
The Bayesian statistical framework provides a systematic approach to enhance the regularization model by incorporating prior information about the desired solution. For the Bayesian linear inverse problems with Gaussian noise and Gaussian…
Gravity inversion is the problem of estimating subsurface density distributions from observed gravitational field data. We consider the two-dimensional (2D) case, in which recovering density models from one-dimensional (1D) measurements…
This manuscript is designed to introduce students in applied mathematics and data science to the concept of regularization for ill-posed inverse problems. Construct a mathematical model that describes how an image gets blurred. Convert a…
We consider regularized least-squares problems of the form $\min_{x} \frac{1}{2}\Vert Ax - b\Vert_2^2 + \mathcal{R}(Lx)$. Recently, Zheng et al., 2019, proposed an algorithm called Sparse Relaxed Regularized Regression (SR3) that employs a…
Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…
The composite $L_q~(0<q<1)$ minimization problem over a general polyhedron has received various applications in machine learning, wireless communications, image restoration, signal reconstruction, etc. This paper aims to provide a…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
Diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency. In this work, we identify a corrector kernel…
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 extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
Numerical experiments in literature on compressed sensing have indicated that the reweighted $l_1$ minimization performs exceptionally well in recovering sparse signal. In this paper, we develop exact recovery conditions and algorithm for…
We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. Focusing on data matrices that are simultaneously row-sparse and low-rank, we propose…