Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially (i) gains with different amplitude and the same phase, (ii) gains with the same amplitude and different phase and (iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided

ECG Signal Reconstruction on the IoT-Gateway and Efficacy of Compressive Sensing Under Real-time Constraints

Remote health monitoring is becoming indispensable, though, Internet of Things (IoTs)-based solutions have many implementation challenges, including energy consumption at the sensing node, and delay and instability due to cloud computing. Compressive sensing (CS) has been explored as a method to extend the battery lifetime of medical wearable devices. However, it is usually associated with computational complexity at the decoding end, increasing the latency of the system. Meanwhile, mobile processors are becoming computationally stronger and more efficient. Heterogeneous multicore platforms (HMPs) offer a local processing solution that can alleviate the limitations of remote signal processing. This paper demonstrates the real-time performance of compressed ECG reconstruction on ARM's big.LITTLE HMP and the advantages they provide as the primary processing unit of the IoT architecture. It also investigates the efficacy of CS in minimizing power consumption of a wearable device under real-time and hardware constraints. Results show that both the orthogonal matching pursuit and subspace pursuit reconstruction algorithms can be executed on the platform in real time and yield optimum performance on a single A15 core at minimum frequency. The CS extends the battery life of wearable medical devices up to 15.4% considering ECGs suitable for wellness applications and up to 6.6% for clinical grade ECGs. Energy consumption at the gateway is largely due to an active internet connection; hence, processing the signals locally both mitigates system's latency and improves gateway's battery life. Many remote health solutions can benefit from an architecture centered around the use of HMPs, a step toward better remote health monitoring systems.Peer reviewedFinal Published versio