Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.

Structured Compressed Sensing: From Theory to Applications

Image compression algorithms convert high-resolution images into a relatively small bit streams in effect turning a large digital data set into a substantially smaller one. This article introduces compressive sampling and recovery using convex programming.

Imaging via Compressive Sampling

The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results.

Signal Processing With Compressive Measurements

The particle filter (PF) was introduced in 1993 as a numerical approximation to the nonlinear Bayesian filtering problem, and there is today a rather mature theory as well as a number of successful applications described in literature. This tutorial serves two purposes: to survey the part of the theory that is most important for applications and to survey a number of illustrative positioning applications from which conclusions relevant for the theory can be drawn. The theory part first surveys the nonlinear filtering problem and then describes the general PF algorithm in relation to classical solutions based on the extended Kalman filter (EKF) and the point mass filter (PMF). Tuning options, design alternatives, and user guidelines are described, and potential computational bottlenecks are identified and remedies suggested. Finally, the marginalized (or Rao-Blackwellized) PF is overviewed as a general framework for applying the PF to complex systems. The application part is more or less a stand-alone tutorial without equations that does not require any background knowledge in statistics or nonlinear filtering. It describes a number of related positioning applications where geographical information systems provide a nonlinear measurement and where it should be obvious that classical approaches based on Kalman filters (KFs) would have poor performance. All applications are based on real data and several of them come from real-time implementations. This part also provides complete code examples.

/pdf/particle-filter-theory-and-practice-with-positioning-3ub8asx2jb.pdf

Particle filter theory and practice with positioning applications

Linköping University Post Print Particle Filter Theory and Practice with Positioning Applications

This paper demonstrates a computational image sensor capable of implementing compressive sensing operations. Instead of sensing raw pixel data, this image sensor projects the image onto a separable 2-D basis set and measures the corresponding expansion coefficients. The inner products are computed in the analog domain using a computational focal plane and an analog vector-matrix multiplier (VMM). This is more than mere postprocessing, as the processing circuity is integrated as part of the sensing circuity itself. We implement compressive imaging on the sensor by using pseudorandom vectors called noiselets for the measurement basis. This choice allows us to reconstruct the image from only a small percentage of the transform coefficients. This effectively compresses the image without any digital computation and reduces the throughput of the analog-to-digital converter (ADC). The reduction in throughput has the potential to reduce power consumption and increase the frame rate. The general architecture and a detailed circuit implementation of the image sensor are discussed. We also present experimental results that demonstrate the advantages of using the sensor for compressive imaging rather than more traditional coded imaging strategies.

Compressive Sensing on a CMOS Separable-Transform Image Sensor

Field-programmable analog arrays (FPAAs) provide a method for rapidly prototyping analog systems. Currently available commercial and academic FPAAs are typically based on operational amplifiers (or other similar analog primitives) with only a few computational elements per chip. While their specific architectures vary, their small sizes and often restrictive interconnect designs leave current FPAAs limited in functionality and flexibility. For FPAAs to enter the realm of large-scale reconfigurable devices such as modern field-programmable gate arrays (FPGAs), new technologies must be explored to provide area-efficient accurately programmable analog circuitry that can be easily integrated into a larger digital/mixed-signal system. Recent advances in the area of floating-gate transistors have led to a core technology that exhibits many of these qualities, and current research promises a digitally controllable analog technology that can be directly mated to commercial FPGAs. By leveraging these advances, a new generation of FPAAs is introduced in this paper that will dramatically advance the current state of the art in terms of size, functionality, and flexibility. FPAAs have been fabricated using floating-gate transistors as the sole programmable element, and the results of characterization and system-level experiments on the most recent FPAA are shown.

https://knowledge.e.southern.edu/cgi/viewcontent.cgi?article=1005&context=facworks_comp

Large-scale field-programmable analog arrays for analog signal processing

This paper discusses the application of a computational image sensor, capable of performing separable 2-D transforms on images in the analog domain, to compressive sensing. Instead of sensing and transmitting raw pixel data, this image sensor first projects the image onto a separable 2-D basis set. The inner products computed in these projections are computed in the analog domain using a computational focal-plane and a computational analog vector-matrix multiplier. Since this operation is performed in the analog domain, components such as the analog-to-digital converters can be taxed less when a only subset of correlations are performed. Compressed sensing theory prescribes the use of a pseudo-random, incomplete basis set, allowing for sampling at less than the Nyquist rate. This can reduce power consumption or increase frame rate.

/pdf/compressive-sensing-on-a-cmos-separable-transform-image-3bmpvwwg00.pdf

Compressive sensing on a CMOS separable transform image sensor

A long-term offset cancellation scheme that enables continuous-time amplifier operation is described. Offset cancellation is achieved by programming floating-gate transistors that form an integral part of the amplifier's architecture. The offset voltage of a single-stage folded cascode amplifier has been programmed to a minimum of plusmn25 muV in a 0.5 mum digital CMOS process. The long-term offset voltage drift has been calculated to be less than 0.5 muV over a period of 10 years at 55degC from a thermionic emission model for floating-gate charge loss. The offset voltage varies by a maximum of 130 muV over a temperature range of 170degC, thereby making this a viable approach to offset cancellation

A Precision CMOS Amplifier Using Floating-Gate Transistors for Offset Cancellation

In most reconfigurable systems, such as FPAAs and FPGAs, the switch element and its associated memory cell is a necessary overhead for performing computation with the active components. However, floating gate based switches in large-scale FPAAs can be programmed anywhere between simple "off" and "on" connections, which allows these programmable conductances to be used as computational elements within synthesized circuits. This decreases the notion of switches as computational dead weight and increases the potential computational area efficiency within FPAAs

J.D. Gray

Papers

Compressive Sensing on a CMOS Separable-Transform Image Sensor

Large-scale field-programmable analog arrays for analog signal processing

Compressive sensing on a CMOS separable transform image sensor

A Precision CMOS Amplifier Using Floating-Gate Transistors for Offset Cancellation

Programmable Floating Gate FPAA Switches Are Not Dead Weight