Contents I. Introduction
CS has emerged as a revolutionary signal processing technique that holds immense potential in various biomedical ap-plications, including electrocardiogram (ECG or EKG), elec-troencephalogram (EEG), and electromyogram (EMG) signal processing [1]. CS overcomes the traditional Shannon-Nyquist Sampling theorem, which states that a signal should be ac-quired first by sampling it at the rate “twice of the maximum original signal frequency”. Then it is compressed for signal transmission through a wireless channel and additional encryption is required if the signal needs to be secured. In contrast, CS directly converts analog signals to information and enables the simultaneous achievement of sampling, compression, and encryption, making it particularly attractive for applications in the realm of the Internet of Things (IoT) [2]–[6]. In this regard, Y. Zhang et al. [7] presented a comprehensive survey of secure wireless communications using CS techniques. It exploits the security potential of CS with different random measurement matrices and explores its applications in var-ious wireless communication scenarios. G. Kuldeep et al. [8] presented a novel approach for secure and efficient data transmission in IoT applications and demonstrate a multi-class encryption scheme that allows the cloud to perform sparse signal recovery without compromising data privacy. According to the results and authors' recommendations, CS-based security techniques are more reliable in IoT applications. In terms of the Internet of Medical Things (IoMT), where security and energy efficiency are of paramount importance, CS can be considered a powerful cryptosystem capable of fulfilling these vital requirements while ensuring the confi-dentiality of the sampling and measurement matrix. In this regard, H. Zhang et al. [9] proposed a low-cost and confidential electrocardiogram (ECG) acquisition framework for wireless body area networks (WBANs). The approach combines CS for low-cost signal acquisition and cryptographic techniques to enhance the framework's confidentiality. Authors utilize a RIPless measurement matrix and a chaotic systems as security key to resist plaintext attacks and the experimental results demonstrated the effectiveness of the proposed framework in signal reconstruction and security. Authors in [10] proposed a method of secure CS for physiological signals in healthcare IoT applications that aims to achieve efficient and secure data transmission of physiological signals, which combines CS and encryption techniques to ensure data privacy and minimize data transmission and storage requirements. More-over, authors in [11] presented a hardware architecture design for a secure sensor node to sense ECG signals in Wireless BAN. The design uses CS with a binary sparse measurement matrix to minimize structural complexity and achieve 80-bit security. By performing compression and encryption in a single step, the hardware complexity is reduced. Additionally, BCH (Bose-Chaudhuri-Hocquenghem) coding is employed for forward error correction to ensure signal quality during wireless communication. In addition, the authors in [12] in-troduced a rapid and lightweight encryption technique suitable for resource-constrained edge devices. The method employs a deterministic binary block diagonal (DBBD) matrix, DCT, and Linear program for sensing, sparse representation, and reconstruction, respectively. Numerous studies have explored different methods for secure CS recovery in biomedical sig-nals [13]–[15]. Furthermore, certain papers have specifically focused on strategies to maintain the confidentiality of ECG data during transmission [16], [17]. Although, the proposed approaches in the literature show promising results in terms of signal compression and security, there are a few limitations of the studies such as: scalability, lack of performance evaluation under real-world conditions, limited security analysis with different measurement matrices and comparison with existing approaches. Most of the researchers work on specific applications and used preprocessed data. In this paper, we introduce a novel approach for secure and energy -efficient ECG signal monitoring. Our approach integrates two encryption methods of secure data transmission, employs three distinct sensing or encryption matrices, and utilizes a single reconstruction algorithm. Our contributions in this paper are outlined as follows:
Performance comparison for three different sensing ma-trices in the ECG use case: Random Gaussian Matrix (RGM), Random Binary Matrix with density of 1 's being 20% RBM(d=20%), and Random Binary Matrix with density of 1's being 10% RBM(d=10%). We experi-mented with Compression Ratios (CR) ranging from 0.1 (i.e. 90% data reduction) to 0.9 (10% data reduction). These compressed signals, which also serve as encrypted signals, are transmitted over a wireless channel and reconstructed using the Block Sparse Bayesian Learning algorithm (BSBL) algorithm.
Introduction of a two-step approach, in which, the ECG signals are encrypted using a random permutation. Post encryption, they are compressed using the aforementioned sensing matrices. At the receiver's end, the signal undergoes also a two-step process: it is first decompressed using the BSBL algorithm and subsequently decrypted using the key.
