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This paper introduces a novel approach to constructing binary sensing matrices for compressive sensing using a learning-based technique that leverages mathematical properties instead of traditional datasets. By employing a neural network framework that focuses on minimizing mutual coherence, the authors achieve perfect signal recovery while significantly reducing computational costs. The method's uniqueness lies in its ability to define the loss function through mathematical properties, marking a substantial advancement in the design of sensing matrices for real-world applications.
Achieving perfect signal recovery with a neural network that constructs low mutual coherence binary sensing matrices without relying on large datasets could revolutionize compressive sensing techniques.
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.
