Rakeness-Based Design of Low-Complexity Compressed Sensing

Abstract

Compressed Sensing (CS) can be introduced in the processing chain of a sensor node as a mean to globally reduce its operating cost, while maximizing the quality of the acquired signal. We exploit CS as a simple early-digital compression stage that performs a multiplication of the signal by a matrix. The operating costs (e.g., the consumed power) of such an encoding stage depend on the number of rows of the matrix, but also on the value and position of the rows' coefficients. Our novel design flow yields optimized sparse matrices with very few rows. It is a non-trivial extension of the rakeness-based approach to CS and yields an extremely lightweight stage implemented by a very small number of possibly signed sums with an excellent compression performance. By means of a general signal model we explore different corners of the design space and show that, for example, our method is capable of compressing the signal by a factor larger than 2.5 while not considering 30% of the original samples (so that they may not be acquired at all, leaving the analog front-end and ADC stages inactive) and by processing each of the considered samples with not more than three signed sums

Energy Analysis of Decoders for Rakeness-Based Compressed Sensing of ECG Signals

“…This is the main reason why we may expect higher performance with rakeness-based CS with respect to other signal agnostic techniques, at least when localization is strong enough. For the ECG signals, in [21] it is also proved that rakeness-based CS outperforms the approch discussed in [27] which, similar to our, is suitable for binary sensing matrices. Others techniques (like [25], [26]) have a further limitation, both approaches are not compatible with the antipodal symbol constraints, thus requiring full multipliers at the encoder side.…”

“…Note that the adoption of a decoder properly specialized on the ECG reconstruction does not imply that the rakeness-based CS is useless. As proved in [21] for BSBL and WLM, using an adapted sensing matrix following the rakeness design-flow further increases the performance of a properly specialized decoding stage. Among the mentioned approach, we focus here on WLM.…”

An Energy-Efficient Multi-Sensor Compressed Sensing System Employing Time-Mode Signal Processing Techniques

“…In standard CS theory, this is ensured by generating entries of A as instances of independent and identically distributed random variables [6]. Along all possible CS encoders already proposed in the literature, circuit implementations that adopt either antipodal or ternary random sensing matrices are more advantageous [8], [11]- [13]. This means that the sensing matrix entries are still random but are limited to either A j,k ∈ {−1, 1} or A j,k ∈ {−1, 0, 1} where, in the latter case, an increase in the number of zeros implies a reduction in the number of operations needed to compute y.…”

“…where p i (•) and n i (•) map the positions of positive and negative entries of the i-th row of A, respectively. The CS approach was expanded in [8], [14] where the authors proposed a soft adaptation of the second-order statistics of the sensing matrix rows to the second-order statistics of the acquired class of signals, and this method is called rakeness-based CS.…”

“…The obtained output, the measurement vector, is then transmitted to a decoder block to recover the original signal. Alternatively, CS can be used as a low power compression scheme after signal digitization [7], [8]. The research work presented here focuses on multi-channel electrode arrays that characterize a huge set of biomedical applications [7], [9], [10], where the input signal is the collection of readings.…”