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In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…

Computer Vision and Pattern Recognition · Computer Science 2023-08-11 Iaroslav Koshelev , Stamatios Lefkimmiatis

The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…

Numerical Analysis · Mathematics 2024-11-06 Nian-Ci Wu , Chengzhi Liu , Yatian Wang , Qian Zuo

Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…

Numerical Analysis · Mathematics 2025-01-20 Erin Carson , Ieva Daužickaitė

We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…

Numerical Analysis · Mathematics 2018-01-30 Thomas Führer

Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…

Information Theory · Computer Science 2021-02-17 Pengxia Wu , Hui Ma , Julian Cheng

Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…

Computational Engineering, Finance, and Science · Computer Science 2018-04-17 C. P. E. Agbachi

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Computer Vision and Pattern Recognition · Computer Science 2015-04-29 Chen Chen , Junzhou Huang , Lei He , Hongsheng Li

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…

Machine Learning · Computer Science 2024-01-19 Christian Kümmerle , Johannes Maly

Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…

Optimization and Control · Mathematics 2015-03-17 Mazen Al Borno

Model reduction simplifies complex dynamical systems while preserving essential properties. This paper revisits a recently proposed system-theoretic framework for least squares moment matching. It interprets least squares model reduction in…

Optimization and Control · Mathematics 2025-05-28 Alberto Padoan

In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…

Optimization and Control · Mathematics 2025-12-25 Junpeng Zhou , Na Zhang , Qia Li

In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm is guaranteed to have an exact recovery from $O(s\log n)$…

Numerical Analysis · Mathematics 2022-11-23 Jian-Feng Cai , Yuling Jiao , Xiliang Lu , Juntao You

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

Machine Learning · Computer Science 2024-07-17 Roberto Esposito , Mattia Cerrato , Marco Locatelli

Future services demand high data rate and quality. Thus, it is necessary to define new and robust algorithms to equalize channels and reduce noise in communications. Nowadays, new equalization algorithms are being developed to optimize the…

Information Theory · Computer Science 2012-08-13 Sanaz Moshirian , Soheil Ghadami , Mohammad Havaei

Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…

Signal Processing · Electrical Eng. & Systems 2022-06-28 Jonas Kornprobst , Alexander Paulus , Josef Knapp , Thomas F. Eibert

We propose a two-stage penalized least squares method to build large systems of structural equations based on the instrumental variables view of the classical two-stage least squares method. We show that, with large numbers of endogenous…

Methodology · Statistics 2018-07-31 Chen Chen , Min Ren , Min Zhang , Dabao Zhang

The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…

Optimization and Control · Mathematics 2015-02-27 Benjamin Lenoir

For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…

Signal Processing · Electrical Eng. & Systems 2023-11-30 Carter Lyons , Raghu G. Raj , Margaret Cheney

Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…

Machine Learning · Computer Science 2018-10-08 Michał Dereziński , Manfred K. Warmuth , Daniel Hsu

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

Statistics Theory · Mathematics 2018-10-16 Michael Krikheli , Amir Leshem