Friday, November 05, 2010

CS: A Real-Time Compressed Sensing-Based Personal Electrocardiogram Monitoring System, From Sparse Signals to Sparse Residuals for Robust Sensing

Here is more detail on the FISTA reconstruction algorithm running on a jailbroken iPhone. From Pierre Vandergheynst twitter's stream, the implementation that received so much attention in:
Wireless body sensor networks (WBSN) hold the promise to enable next-generation patient-centric tele-cardiology systems. A WBSN-enabled electrocardiogram (ECG) monitor consists of wearable, miniaturized and wireless sensors able to measure and wirelessly report cardiac signals to a WBSN coordinator, which is responsible for reporting them to the tele-health provider. However, state-of-the-art WBSN-enabled ECG monitors still fall short of the required functionality, miniaturization and energy efficiency. Among others, energy efficiency can be significantly improved through embedded ECG compression, which reduces airtime over energy-hungry wireless links. In this paper, we propose a novel real-time energy-aware ECG monitoring system based on the emerging compressed sensing (CS) signal acquisition/compression paradigm for WBSN applications. For the first time, CS is demonstrated as an advantageous real-time and energy-efficient ECG compression technique, with a computationally light ECG encoder on the state-of-the-art ShimmerTM wearable sensor node and a realtime decoder running on an iPhone (acting as a WBSN coordinator). Interestingly, our results show an average CPU usage of less than 5% on the node, and of less than 30% on the iPhone.
Here is the attendant video:

One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while specifying the unreliable ones is critical for robust sensing. This sensing task is formulated here as that of finding the maximum number of feasible subsystems of linear equations, and proved to be NP-hard. Useful links are established with compressive sampling, which aims at recovering vectors that are sparse. In contrast, the signals here are not sparse, but give rise to sparse residuals. Capitalizing on this form of sparsity, four sensing schemes with complementary strengths are developed. The first scheme is a convex relaxation of the original problem expressed as a second-order cone program (SOCP). It is shown that when the involved sensing matrices are Gaussian and the reliable measurements are sufficiently many, the SOCP can recover the optimal solution almost surely. The second scheme is obtained by replacing the initial objective function with a concave one. The third and fourth schemes are tailored for noisy sensor data. The noisy case is cast as a combinatorial problem that is subsequently surrogated by a (weighted) SOCP. Interestingly, the derived cost functions fall into the framework of robust multivariate linear regression, while an efficient block-coordinate descent algorithm is developed for their minimization. The robust sensing capabilities of all schemes are verified by simulated tests.

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