相关论文: Towards Designing Optimal Sensing Matrices for Gen…

This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…

Exceptional points (EPs) in non-Hermitian photonic systems enable unconventional control of wave amplitude and phase. However, identifying the EPs in multidimensional parameter space of a system can be nontrivial and, in some cases, even…

We consider functional data where an underlying smooth curve is composed not just with errors, but also with irregular spikes. We propose an approach that, combining regularized spline smoothing and an Expectation-Maximization algorithm,…

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

We study estimation of the covariance matrix under relative condition number loss $\kappa(\Sigma^{-1/2} \hat{\Sigma} \Sigma^{-1/2})$, where $\kappa(\Delta)$ is the condition number of matrix $\Delta$, and $\hat{\Sigma}$ and $\Sigma$ are the…

Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…

In this paper, we develop a framework to design sensing matrices for compressive sensing applications that lead to good mean squared error (MSE) performance subject to sensing cost constraints. By capitalizing on the MSE of the oracle…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…

We investigate the problem of approximate Bayesian inference for a general class of observation models by means of the expectation propagation (EP) framework for large systems under some statistical assumptions. Our approach tries to…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…

In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…

We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…

Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing…

Spiking Neural Networks (SNNs), particularly Spiking Transformers, offer energy-efficient processing of event-based sensor data for healthcare applications. Yet current architectures are rigid: they are trained and deployed as static…

Our objective is to efficiently design a robust projection matrix $\Phi$ for the Compressive Sensing (CS) systems when applied to the signals that are not exactly sparse. The optimal projection matrix is obtained by mainly minimizing the…

The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional…

Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing…

Optical systems are a main platform for quantum information processing. A main challenge is information loss due to scattering in unmonitored modes. These losses are modeled as state-independent beam-splitter interactions, with a thermal…