通过无限维压缩感知进行热源定位

Randomness and isometries in echo state networks and compressed sensing

Although largely different concepts, echo state networks and compressed sensing models both rely on collections of random weights; as the reservoir dynamics for echo state networks, and the sensing coefficients in compressed sensing. Several methods for generating the random matrices and metrics to indicate desirable performance are well-studied in compressed sensing, but less so for echo state networks. This work explores any overlap in these compressed sensing methods and metrics for application to echo state networks. Several methods for generating the random reservoir weights are considere…

An enhanced decoding algorithm for coded compressed sensing

Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to machine-type communications. Coded compressed sensing uses a divide-and-conquer approach to break the sparse recovery task into sub-components whose dimensions are amenable to conventional compressed sensing solvers. The recovered fragments are then stitched together using a low complexity decoder. This article introduces an enhanced decoding algorithm for coded compre…

Compressed Sensing Constant Modulus Constrained Projection Matrix Design and High-Resolution DoA Estimation Methods

This paper proposes a compressed sensing-based high-resolution direction-of-arrival estimation method called gradient orthogonal matching pursuit (GOMP). It contains two main steps: a sparse coding approximation step using the well-known OMP method and a sequential iterative refinement step using a newly proposed gradient-descent method. To enhance the recoverability, we further propose an efficient projection matrix design method, which considers the constant modulus constraints imposed by the projection matrix hardware components. Simulation results show the effectiveness of the proposed met…

相位压缩感知中的相变现象

Phase Transitions in Phase-Only Compressed Sensing

本文研究相位压缩感知的相变位置，证明其由下降锥的统计维数决定，并给出稀疏信号和低秩矩阵的精确公式，表明相位测量比线性测量更高效，反驳了先前猜想。

Variational Quantum Compressed Sensing for Joint User and Channel State Acquisition in Grant-Free Device Access Systems

This paper introduces a new quantum computing framework integrated with a two-step compressed sensing technique, applied to a joint channel estimation and user identification problem. We propose a variational quantum circuit (VQC) design as a new denoising solution. For a practical grant-free communications system having correlated device activities, variational quantum parameters for Pauli rotation gates in the proposed VQC system are optimized to facilitate to the non-linear estimation. Numerical results show that the VQC method can outperform modern compressed sensing techniques using an el…

Robust one-bit compressed sensing with partial circulant matrices

We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled circulant matrix) and is robust to analog pre-quantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed had the measurement matrix been Gaussian and the noisy analog measurements been given as data.