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Pruning the weights of neural networks is an effective and widely-used technique for reducing model size and inference complexity. We develop and test a novel method based on compressed sensing which combines the pruning and training into a…
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…
It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation.A key insight explored in this work is that the loop-closing event inherently occurs sparsely, that is, the image currently being…
This paper focuses on prior information for improved sparsity reconstruction in electrical impedance tomography with partial data, i.e. data measured only on subsets of the boundary. Sparsity is enforced using an $\ell_1$ norm of the basis…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
In this paper, we propose a non-convex formulation to recover the authentic structure from the corrupted real data. Typically, the specific structure is assumed to be low rank, which holds for a wide range of data, such as images and…
Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate…
Augmenting a smooth cost function with an $\ell_1$ penalty allows analysts to efficiently conduct estimation and variable selection simultaneously in sophisticated models and can be efficiently implemented using proximal gradient methods.…
Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some…
Sparsification of neural networks is one of the effective complexity reduction methods to improve efficiency and generalizability. We consider the problem of learning a one hidden layer convolutional neural network with ReLU activation…
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 study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
Deep models trained on large amounts of data often incorporate implicit biases present during training time. If later such a bias is discovered during inference or deployment, it is often necessary to acquire new data and retrain the model.…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
For data with high-dimensional covariates but small to moderate sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of…
$\ell_1$ mean filtering is a conventional, optimization-based method to estimate the positions of jumps in a piecewise constant signal perturbed by additive noise. In this method, the $\ell_1$ norm penalizes sparsity of the first-order…
The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models,…
This paper is intended to solve the nonconvex $\ell_{p}$-ball constrained nonlinear optimization problems. An iteratively reweighted method is proposed, which solves a sequence of weighted $\ell_{1}$-ball projection subproblems. At each…