发表机构
Shiv Nadar Institution of Eminence; Indian Statistical Institute（希夫·纳达尔卓越学院; 印度统计研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种不依赖数据集的神经网络框架，利用互相干数学性质定义损失函数，构建低互相干二元感知矩阵，降低计算成本并提升通用性与鲁棒性。
AI 中文摘要
本研究构建了感知矩阵，这是压缩感知技术成功的关键。我们选择基于学习的技术来构建感知矩阵，该技术的新颖性和独特之处在于：它不使用任何数据集，也不针对特定应用，而是利用数学性质/约束来构建感知矩阵，以实现信号的完美恢复。信号的完美恢复是现实应用中一个古老且仍极具挑战性的问题。21世纪初，压缩感知成为用于稀疏信号完美恢复的流行数学工具，该技术的核心是构建满足受限等距性质（RIP）、零空间性质（NSP）和火花性质（SP）等特殊性质的感知矩阵。所有这些性质均为NP难问题，因此求解具有计算挑战性。对于所有实际用途，感知矩阵的构建需要实现低互相干，以达到信号的完美恢复。我们使用神经网络构建感知矩阵，该框架生成具有低互相干的二元感知矩阵，矩阵元素通过共享的底层规则生成。所提出的架构简单，不使用大规模训练数据集，这种独特性和新颖性大幅降低了计算成本，且在文献中首次使用数学性质来定义损失函数。本研究在神经网络框架中使用了互相干性质，该神经网络框架具有通用性、鲁棒性，且降低了存储需求。
英文摘要
In this research work, we are constructing the sensing matrix, which is essential for the success of the compressive sensing technique. We have chosen a learning-based technique for the construction of the sensing matrix. The novelty and uniqueness of the proposed technique is that it does not use any data set and also does not use a specific application. It uses the mathematical property/constraint for the construction of the sensing matrix for the perfect recovery of the signal. The perfect recovery of signals is an old and still very challenging problem in real-world applications. In late 2000, compressive sensing became a popular mathematical tool for the perfect recovery of sparse signals. The core of the compressive technique is the construction of the sensing matrix, which satisfies certain special properties such as restricted isometry property (RIP), null space property (NSP), and spark property (SP). All these properties are NP-hard problems and hence computationally challenging to solve. For all practical purposes, the construction of the sensing matrix needs to achieve low mutual coherence to achieve the perfect recovery of the signals. We have used a neural network for the construction of the sensing matrix, and this framework constructs a binary sensing matrix with low mutual coherence. The entries in the matrix are generated through a shared underlying rule. The proposed architecture is simple and does not use large-scale training data sets. Such uniqueness and novelty bring a drastic reduction in computational cost, and also, for the first time in literature, the use of a mathematical property for defining the loss function. In this proposed research work, the mutual coherence property has been used in the neural network framework. Such a neural network framework brings generality, robustness, and reduces storage requirements.
Comments25 pages, 18 figures
