Related papers: Weighed l1 on the simplex: Compressive sensing mee…
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…
Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is $\ell_p$ regularization. However, it may encounter optimization instability due to the unbounded gradients when…
We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…
Local polynomial regression struggles with several challenges when dealing with sparse data. The difficulty in capturing local features of the underlying function can lead to a potential misrepresentation of the true relationship.…
In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…
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…
Reliable and energy-efficient wireless data transmission remains a major challenge in resource-constrained wireless neural recording tasks, where data compression is generally adopted to relax the burdens on the wireless data link.…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
In this paper, we propose a semi-supervised dictionary learning method that uses both the information in labelled and unlabelled data and jointly trains a linear classifier embedded on the sparse codes. The manifold structure of the data in…
We propose an sparse Bayesian learning (SBL)-based method that leverages group sparsity and multiple parameterized dictionaries to detect the relevant dictionary entries and estimate their continuous parameters by combining data from…
The recovery of approximately sparse or compressible coefficients in a Polynomial Chaos Expansion is a common goal in modern parametric uncertainty quantification (UQ). However, relatively little effort in UQ has been directed toward…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
Applying compressive sensing (CS) allows for sub-Nyquist sampling in several application areas in 5G and beyond. This reduces the associated training, feedback, and computation overheads in many applications. However, the applicability of…
This paper considers the problem of simultaneously learning the Sensing Matrix and Sparsifying Dictionary (SMSD) on a large training dataset. To address the formulated joint learning problem, we propose an online algorithm that consists of…
Recently, convolutional auto-encoders (CAE) were introduced for image coding. They achieved performance improvements over the state-of-the-art JPEG2000 method. However, these performances were obtained using massive CAEs featuring a large…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
Dictionary learning for sparse representations has been successful in many reconstruction tasks. Simplicial learning is an adaptation of dictionary learning, where subspaces become clipped and acquire arbitrary offsets, taking the form of…