Partitioned Compressive Sensing with Neighbor-Weighted Decoding

Compressive sensing has gained momentum in recent years as an exciting new theory in signal processing with several useful applications. It states that signals known to have a sparse representation may be encoded and later reconstructed using a small number of measurements, approximately proportional to the signal s sparsity rather than its size. This paper addresses a critical problem that arises when scaling compressive sensing to signals of large length: that the time required for decoding becomes prohibitively long, and that decoding is not easily parallelized. We describe a method for partitioned compressive sensing, by which we divide a large signal into smaller blocks that may be decoded in parallel. However, since this process requires a signi cant increase in the number of measurements needed for exact signal reconstruction, we focus on mitigating artifacts that arise due to partitioning in approximately reconstructed signals. Given an error-prone partitioned decoding, we use large magnitude components that are detected with highest accuracy to in uence the decoding of neighboring blocks, and call this approach neighbor-weighted decoding. We show that, for applications with a prede ned error threshold, our method can be used in conjunction with partitioned compressive sensing to improve decoding speed, requiring fewer additional measurements than unweighted or locally-weighted decoding.Engineering and Applied Science

Partitioned Compressive Sensing with Neighbor-Weighted Decoding

Abstract—Compressive sensing has gained momentum in recent years as an exciting new theory in signal processing with several useful applications. It states that signals known to have a sparse representation may be encoded and later reconstructed using a small number of measurements, approximately proportional to the signal’s sparsity rather than its size. This paper addresses a critical problem that arises when scaling compressive sensing to signals of large length: that the time required for decoding becomes prohibitively long, and that decoding is not easily parallelized. We describe a method for partitioned compressive sensing, by which we divide a large signal into smaller blocks that may be decoded in parallel. However, since this process requires a significant increase in the number of measurements needed for exact signal reconstruction, we focus on mitigating artifacts that arise due to partitioning in approximately reconstructed signals. Given an error-prone partitioned decoding, we use large magnitude components that are detected with highest accuracy to influence the decoding of neighboring blocks, and call this approach neighbor-weighted decoding. We show that, for applications with a predefined error threshold, our method can be used in conjunction with partitioned compressive sensing to improve decoding speed, requiring fewer additional measurements than unweighted or locally-weighted decoding. I

Leveraging Signal Transfer Characteristics and Parasitics of Spintronic Circuits for Area and Energy-Optimized Hybrid Digital and Analog Arithmetic

While Internet of Things (IoT) sensors offer numerous benefits in diverse applications, they are limited by stringent constraints in energy, processing area and memory. These constraints are especially challenging within applications such as Compressive Sensing (CS) and Machine Learning (ML) via Deep Neural Networks (DNNs), which require dot product computations on large data sets. A solution to these challenges has been offered by the development of crossbar array architectures, enabled by recent advances in spintronic devices such as Magnetic Tunnel Junctions (MTJs). Crossbar arrays offer a compact, low-energy and in-memory approach to dot product computation in the analog domain by leveraging intrinsic signal-transfer characteristics of the embedded MTJ devices. The first phase of this dissertation research seeks to build on these benefits by optimizing resource allocation within spintronic crossbar arrays. A hardware approach to non-uniform CS is developed, which dynamically configures sampling rates by deriving necessary control signals using circuit parasitics. Next, an alternate approach to non-uniform CS based on adaptive quantization is developed, which reduces circuit area in addition to energy consumption. Adaptive quantization is then applied to DNNs by developing an architecture allowing for layer-wise quantization based on relative robustness levels. The second phase of this research focuses on extension of the analog computation paradigm by development of an operational amplifier-based arithmetic unit for generalized scalar operations. This approach allows for 95% area reduction in scalar multiplications, compared to the state-of-the-art digital alternative. Moreover, analog computation of enhanced activation functions allows for significant improvement in DNN accuracy, which can be harnessed through triple modular redundancy to yield 81.2% reduction in power at the cost of only 4% accuracy loss, compared to a larger network. Together these results substantiate promising approaches to several challenges facing the design of future IoT sensors within the targeted applications of CS and ML

Compressive Sensing and Recovery of Structured Sparse Signals

In the recent years, numerous disciplines including telecommunications, medical imaging, computational biology, and neuroscience benefited from increasing applications of high dimensional datasets. This calls for efficient ways of data capturing and data processing. Compressive sensing (CS), which is introduced as an efficient sampling (data capturing) method, is addressing this need. It is well-known that the signals, which belong to an ambient high-dimensional space, have much smaller dimensionality in an appropriate domain. CS taps into this principle and dramatically reduces the number of samples that is required to be captured to avoid any distortion in the information content of the data. This reduction in the required number of samples enables many new applications that were previously infeasible using classical sampling techniques. Most CS-based approaches take advantage of the inherent low-dimensionality in many datasets. They try to determine a sparse representation of the data, in an appropriately chosen basis using only a few significant elements. These approaches make no extra assumptions regarding possible relationships among the significant elements of that basis. In this dissertation, different ways of incorporating the knowledge about such relationships are integrated into the data sampling and the processing schemes. We first consider the recovery of temporally correlated sparse signals and show that using the time correlation model. The recovery performance can be significantly improved. Next, we modify the sampling process of sparse signals to incorporate the signal structure in a more efficient way. In the image processing application, we show that exploiting the structure information in both signal sampling and signal recovery improves the efficiency of the algorithm. In addition, we show that region-of-interest information can be included in the CS sampling and recovery steps to provide a much better quality for the region-of-interest area compared the rest of the image or video. In spectrum sensing applications, CS can dramatically improve the sensing efficiency by facilitating the coordination among spectrum sensors. A cluster-based spectrum sensing with coordination among spectrum sensors is proposed for geographically disperse cognitive radio networks. Further, CS has been exploited in this problem for simultaneous sensing and localization. Having access to this information dramatically facilitates the implementation of advanced communication technologies as required by 5G communication networks