相关论文: A convex program for bilinear inversion of sparse …

We develop a convex framework for spatially varying coefficient quantile regression that, for each predictor, separates a location-invariant \emph{global} effect from a \emph{spatial deviation}. An adaptive group penalty selects whether a…

In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). However, standard spectral methods based on Fourier transforms struggle with problems involving discontinuous…

Sparse learning has been widely studied to capture critical information from enormous data sources in the filed of system identification. Often, it is essential to understand internal working mechanisms of unknown systems (e.g. biological…

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…

We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and $\ell_\infty$-bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex. Using…

Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…

This article discusses the problem of determining whether a given point, or set of points, lies within the convex hull of another set of points in $d$ dimensions. This problem arises naturally in a statistical context when using a…

This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying…

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…

We propose a two-step approach for reconstructing a signal ${\bf x}\in\mathbb{C}^d$ from subsampled short-time Fourier transform magnitude (spectogram) measurements: First, we use an aliased Wigner distribution deconvolution approach to…

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind…

The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…

A robust algorithm is proposed to reconstruct the spatial support and the Lam\'e parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of…

Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…

We propose the framework of dual convexified convolutional neural networks (DCCNNs). In this framework, we first introduce a primal learning problem motivated by convexified convolutional neural networks (CCNNs), and then construct the dual…

It is known that for a certain class of single index models (SIMs) $Y = f(\boldsymbol{X}_{p \times 1}^\intercal\boldsymbol{\beta}_0, \varepsilon)$, support recovery is impossible when $\boldsymbol{X} \sim \mathcal{N}(0, \mathbb{I}_{p \times…

In this paper, we propose and analyze a two-point gradient method for solving inverse problems in Banach spaces which is based on the Landweber iteration and an extrapolation strategy. The method allows to use non-smooth penalty terms,…

We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…