Related papers: 3-D Projected $ L_{1}$ inversion of gravity data
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for $L_1$-norm…
Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…
A generalized unifying approach for $L_{p}$-norm joint inversion of gravity and magnetic data using the cross-gradient constraint is presented. The presented framework incorporates stabilizers that use $L_{0}$, $L_{1}$, and $L_{2}$-norms of…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
Scarcity of hydrocarbon resources and high exploration risks motivate the development of high fidelity algorithms and computationally viable approaches to exploratory geophysics. Whereas early approaches considered least-squares…
Subsurface ore detection is of paramount importance given the gradual depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods.…
The hybrid LSMR algorithm is proposed for large-scale general-form regularization. It is based on a Krylov subspace projection method where the matrix $A$ is first projected onto a subspace, typically a Krylov subspace, which is implemented…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this…
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…
The paper contains several theoretical results related to the weighted nonlinear least-squares problem for low-rank signal estimation, which can be considered as a Hankel structured low-rank approximation problem. A parameterization of the…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…