Related papers: Sparse Reconstruction of Multi-Dimensional Kinetic…
When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…
We study distributed multi-agent large-scale optimization problems, wherein the cost function is composed of a smooth possibly nonconvex sum-utility plus a DC (Difference-of-Convex) regularizer. We consider the scenario where the dimension…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
Signal estimation from incomplete observations improves as more signal structure can be exploited in the inference process. Classic algorithms (e.g., Kalman filtering) have exploited strong dynamic structure for time-varying signals while…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm…
We consider the \textit{phase retrieval} problem of recovering a sparse signal $\mathbf{x}$ in $\mathbb{R}^d$ from intensity-only measurements in dimension $d \geq 2$. Phase retrieval can be equivalently formulated as the problem of…
Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…
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…
Generalizable neural surface reconstruction has become a compelling technique to reconstruct from few images without per-scene optimization, where dense 3D feature volume has proven effective as a global representation of scenes. However,…
Surface reconstruction from magnetic resonance (MR) imaging data is indispensable in medical image analysis and clinical research. A reliable and effective reconstruction tool should: be fast in prediction of accurate well localised and…
Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against…
Monte Carlo methods are state-of-the-art when it comes to dosimetric computations in radiotherapy. However, the execution time of these methods suffers in high-collisional regimes. We address this problem by introducing a kinetic-diffusion…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…
This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a…
Dynamic network reconstruction has been shown to be challenging due to the requirements on sparse network structures and network identifiability. The direct parametric method (e.g., using ARX models) requires a large amount of parameters in…
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…