Related papers: Discrete and Continuous-time Soft-Thresholding wit…
Compressed sensing is a recent set of mathematical results showing that sparse signals can be exactly reconstructed from a small number of linear measurements. Interestingly, for ideal sparse signals with no measurement noise, random…
In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to achieve…
We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…
With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional…
Previous works have shown that the small-scale information of incompressible homogeneous isotropic turbulence (HIT) is fully recoverable as long as sufficient large-scale structures are continuously enforced through temporally continuous…
An important receiver operation is to detect the presence specific preamble signals with unknown delays in the presence of scattering, Doppler effects and carrier offsets. This task, referred to as "link acquisition", is typically a…
This paper studies computationally efficient methods and their minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose two sets of methods, cross-block feature aggregation PCA…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
A class of distributed optimization problem with a globally coupled equality constraint and local constrained sets is studied in this paper. For its special case where local constrained sets are absent, an augmented primal-dual gradient…
We propose a novel convolutional neural network (CNN), called $\Psi$DONet, designed for learning pseudodifferential operators ($\Psi$DOs) in the context of linear inverse problems. Our starting point is the Iterative Soft Thresholding…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be…
We consider the extensively studied problem of $\ell_2/\ell_2$ compressed sensing. The main contribution of our work is an improvement over [Gilbert, Li, Porat and Strauss, STOC 2010] with faster decoding time and significantly smaller…
The linear inverse problem emerges from various real-world applications such as Image deblurring, inpainting, etc., which are still thrust research areas for image quality improvement. In this paper, we have introduced a new algorithm…
This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…
Time-frequency distributions (TFDs) play a vital role in providing descriptive analysis of non-stationary signals involved in realistic scenarios. It is well known that low time-frequency (TF) resolution and the emergency of cross-terms…
High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with…