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An explicit algorithm for the minimization of an $\ell_1$ penalized least squares functional, with non-separable $\ell_1$ term, is proposed. Each step in the iterative algorithm requires four matrix vector multiplications and a single…
Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…
Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…
Recently, it was demonstrated in [CS2012,CS2013] that the robustness of the classical Non-Local Means (NLM) algorithm [BCM2005] can be improved by incorporating $\ell^p (0 < p \leq 2)$ regression into the NLM framework. This general…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
This paper presents novel adaptive reduced-rank filtering algorithms based on joint iterative optimization of adaptive filters. The novel scheme consists of a joint iterative optimization of a bank of full-rank adaptive filters that…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…
Low-rank adaptations (LoRA) are widely used to fine-tune large models across various domains for specific downstream tasks. While task-specific LoRAs are often available, concerns about data privacy and intellectual property can restrict…
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…
An interference-normalised least mean square (INLMS) algorithm for robust adaptive filtering is proposed. The INLMS algorithm extends the gradient-adaptive learning rate approach to the case where the signals are non-stationary. In…
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…
The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…
We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points…
A simple alternative to the conjugate gradient(CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on…
The development of computed tomography (CT) image reconstruction methods that significantly reduce patient radiation exposure while maintaining high image quality is an important area of research in low-dose CT (LDCT) imaging. We propose a…
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples…
We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections, we retrieve familiar weighted least-squares gradients, but…
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…