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The existing healthcare model based on episodic examination or short-term monitoring for disease diagnosis and treatment suffers from the overlook of individual variability and the lack of personal baseline data. Long-term or non-intermittent monitoring is the key to creating the big data of individual health record for studying the variability and obtaining the personal baseline. Recent advances in wireless body area network (WBAN) and bio-sensing techniques have enabled the emergence of miniaturized, non-invasive, cost-effective wireless sensors that can be placed on human bodies for personal health monitoring . Through WBAN and Internet, the monitored data can be transmitted to a near-field mobile device for on-site processing, as well as to remote servers for storage and data analysis. These technology advancements will eventually revolutionize the health related services to become more efficient and economical, benefiting billions of individuals.
One of the key challenges faced by the long-term wireless health monitoring is the energy efficiency of sensing and information transfer. Due to the limited battery capacity of wireless sensors, non-intermittent sensing inevitably increases the frequency of battery recharging or replacement, making it less convenient for practical use. In bio-sensing applications, the energy cost of wireless transmission is about two orders of magnitude greater than other components . This implies that reducing the data size for information transfer is the key to improving the energy efficiency of wearable sensors.
Compressive sensing (CS)  offers a universal and straightforward data encoding scheme that can compress a variety of physiological signals, providing a promising solution to the problem. However, most existing CS frameworks are model-driven and suffer from very limited performance when dealing with physiological signals [4, 5, 6]. The reasons are two-fold. First, conventional CS frameworks employ random Gaussian or Bernoulli sensing matrices that are generated independently from any data, thereby they fail to leverage any particular geometric structure embedded in the signals of interest. This limits the rank of the sensing matrix required for preserving the Restricted Isometry Property (RIP), leading to limited compression ratio (CR). On the other hand, conventional CS frameworks [7, 8, 5] that adopt predetermined basis for reconstruction underestimate the intricacy of philological signals and overlook the criticality of individual variability to signal fidelity, which results in very limited reconstruction performance especially at high CR . Our previous study  has shown that learned dictionaries can better approximate the underlying statistical model of input data. Therefore, they can significantly improve the sparsity of physiological signals as well as reconstruction performance.
There have been some recent work on exploiting data structures for compressive sensing [10, 11, 12]. In , the authors aim to minimize the averaged mutual coherence between sensing matrix and dictionary. The major limitation of this work is that the mutual coherence is not a direct indicator of RIP, so the optimization result is not suitable for sensor applications. In , the authors aim to find a sensing matrix and a dictionary such that the Gram matrix of the product is as close to the identity matrix as possible. The problem is that the Gram matrix can hardly be the identity matrix in practice as is usually over-complete, so the result is sub-optimal. In , the authors aim to preserve the pairwise distance between sample vectors. However, since the NuMax formulation minimizes the transformation distortion against the original signal rather than its sparse coefficient, the trained sensing matrix is not compatible with any over-complete dictionaries. Therefore, these existing approaches are not ideally suitable for the CS of physiological signals in wearable sensing applications.
In this project, we propose a data-driven CS framework that co-optimizes the sensing matrix and the dictionary towards improved restricted isometry property (RIP) and signal sparsity, respectively, by exploiting the intrinsic data structure of physiological signals. Specifically, online dictionary learning (ODL)  is first adopted to train a personalized basis that further improves signal sparsity by capturing the characteristics and individual variability of physiological signals. Based on the learned dictionary, a distortion minimization problem is formulated to construct a near-isometry and low-rank sensing matrix to guarantee a satisfactory recovery performance at improved compression ratios. Overall, the proposed framework keeps the promise to significantly enhance the reconstruction quality and CR trade-off for the CS of physiological signals.
The data-driven nature of the proposed CS framework is very appealing because it fills the gap between the massive medical data and how to utilize them to improve the quality of sensing. The key insight from this study is that the sensor energy efficiency can be enhanced by learning the intrinsic signal structures from big data through cost-effective computation on server systems, rather than doing costly circuit-level development. Moreover, the proposed data-driven framework is equally applicable to a variety of physiological signals and has the potential to be consistently improved as more and more data is collected for training.