Operational Rate-Distortion Performance of Single-source and Distributed Compressed Sensing

We consider correlated and distributed sources without cooperation at the encoder. For these sources, we derive the best achievable performance in the rate-distortion sense of any distributed compressed sensing scheme, under the constraint of high--rate quantization. Moreover, under this model we derive a closed--form expression of the rate gain achieved by taking into account the correlation of the sources at the receiver and a closed--form expression of the average performance of the oracle receiver for independent and joint reconstruction. Finally, we show experimentally that the exploitation of the correlation between the sources performs close to optimal and that the only penalty is due to the missing knowledge of the sparsity support as in (non distributed) compressed sensing. Even if the derivation is performed in the large system regime, where signal and system parameters tend to infinity, numerical results show that the equations match simulations for parameter values of practical interest.Comment: To appear in IEEE Transactions on Communication

Graded quantization for multiple description coding of compressive measurements

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics

Theoretical Analysis of Binary Masks in Snapshot Compressive Imaging Systems

Snapshot compressive imaging (SCI) systems have gained significant attention in recent years. While previous theoretical studies have primarily focused on the performance analysis of Gaussian masks, practical SCI systems often employ binary-valued masks. Furthermore, recent research has demonstrated that optimized binary masks can significantly enhance system performance. In this paper, we present a comprehensive theoretical characterization of binary masks and their impact on SCI system performance. Initially, we investigate the scenario where the masks are binary and independently identically distributed (iid), revealing a noteworthy finding that aligns with prior numerical results. Specifically, we show that the optimal probability of non-zero elements in the masks is smaller than 0.5. This result provides valuable insights into the design and optimization of binary masks for SCI systems, facilitating further advancements in the field. Additionally, we extend our analysis to characterize the performance of SCI systems where the mask entries are not independent but are generated based on a stationary first-order Markov process. Overall, our theoretical framework offers a comprehensive understanding of the performance implications associated with binary masks in SCI systems

Efficient Space-Time Sampling with Pixel-wise Coded Exposure for High Speed Imaging

Cameras face a fundamental tradeoff between spatial and temporal resolution. Digital still cameras can capture images with high spatial resolution, but most high-speed video cameras have relatively low spatial resolution. It is hard to overcome this tradeoff without incurring a significant increase in hardware costs. In this paper, we propose techniques for sampling, representing and reconstructing the space-time volume in order to overcome this tradeoff. Our approach has two important distinctions compared to previous works: (1) we achieve sparse representation of videos by learning an over-complete dictionary on video patches, and (2) we adhere to practical hardware constraints on sampling schemes imposed by architectures of current image sensors, which means that our sampling function can be implemented on CMOS image sensors with modified control units in the future. We evaluate components of our approach - sampling function and sparse representation by comparing them to several existing approaches. We also implement a prototype imaging system with pixel-wise coded exposure control using a Liquid Crystal on Silicon (LCoS) device. System characteristics such as field of view, Modulation Transfer Function (MTF) are evaluated for our imaging system. Both simulations and experiments on a wide range of scenes show that our method can effectively reconstruct a video from a single coded image while maintaining high spatial resolution

Communication channel analysis and real time compressed sensing for high density neural recording devices

Next generation neural recording and Brain- Machine Interface (BMI) devices call for high density or distributed systems with more than 1000 recording sites. As the recording site density grows, the device generates data on the scale of several hundred megabits per second (Mbps). Transmitting such large amounts of data induces significant power consumption and heat dissipation for the implanted electronics. Facing these constraints, efficient on-chip compression techniques become essential to the reduction of implanted systems power consumption. This paper analyzes the communication channel constraints for high density neural recording devices. This paper then quantifies the improvement on communication channel using efficient on-chip compression methods. Finally, This paper describes a Compressed Sensing (CS) based system that can reduce the data rate by > 10x times while using power on the order of a few hundred nW per recording channel