The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1-bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that i.i.d. random Gaussian matrices provide measurement mappings that, with overwhelming probability, achieve nearly optimal error decay. Next, we consider reconstruction robustness to measurement errors and noise and introduce the binary$\epsilon $-stable embedding property, which characterizes the robustness of the measurement process to sign changes. We show that the same class of matrices that provide almost optimal noiseless performance also enable such a robust mapping. On the practical side, we introduce the binary iterative hard thresholding algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.

The recently developed compressive sensing (CS) framework enables the design of sub-Nyquist analog-to-digital converters. Several architectures have been proposed for the acquisition of sparse signals in large swaths of bandwidth. In this paper we consider a more flexible multi-channel signal model consisting of several discontiguous channels where the occupancy of the combined bandwidth of the channels is sparse. We introduce a new compressive acquisition architecture, the compressive multiplexer (CMUX), to sample such signals. We demonstrate that our architecture is CS-feasible and suggest a simple implementation with numerous practical advantages.

This paper develops a new class of algorithms for signal recovery in the distributed compressive sensing (DCS) framework. DCS exploits both intra-signal and inter-signal correlations through the concept of joint sparsity to further reduce the number of measurements required for recovery. DCS is well-suited for sensor network applications due to its universality, computational asymmetry, tolerance to quantization and noise, and robustness to measurement loss. In this paper we propose recovery algorithms for the sparse common and innovation joint sparsity model. Our approach leads to a class of efficient algorithms, the Texas Hold 'Em algorithms, which are scalable both in terms of communication bandwidth and computational complexity.

Wideband analog signals push contemporary analog-to-digital conversion (ADC) systems to their performance limits. In many applications, however, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the band limit, although the locations of the frequencies may not be known a priori. For this type of sparse signal, other sampling strategies are possible. This paper describes a new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components. Let K denote the total number of frequencies in the signal, and let W denote its band limit in hertz. Simulations suggest that the random demodulator requires just O(K log(W/K)) samples per second to stably reconstruct the signal. This sampling rate is exponentially lower than the Nyquist rate of W hertz. In contrast to Nyquist sampling, one must use nonlinear methods, such as convex programming, to recover the signal from the samples taken by the random demodulator. This paper provides a detailed theoretical analysis of the system's performance that supports the empirical observations.

In this paper, we successfully demonstrate the feasibility of hardware implementation of a sub-Nyquist random sampling based analog to information converter (RS-AIC). The RS-AIC is based on the theory of information recovery from random samples using an efficient information recovery algorithm to compute the spectrogram of the signal. Our RS-AIC enables sub-Nyquist acquisition and processing of wideband signals that are sparse in a local Fourier representation. Results from our RS-AIC hardware implementation demonstrate successful reconstruction of signals that are sampled at half the Nyquist-rate while maintaining up to a 51 dB signal-to-noise ratio (SNR), which is equivalent to an 8.5 bit resolution analog to digital converter.

We propose a framework for exploiting dimension-reducing random projections in detection and classification problems. Our approach is based on the generalized likelihood ratio test; in the case of image classification, it exploits the fact that a set of images of a fixed scene under varying articulation parameters forms a low-dimensional, nonlinear manifold. Exploiting recent results showing that random projections stably embed a smooth manifold in a lower-dimensional space, we develop the multiscale smashed filter as a compressive analog of the familiar matched filter classifier. In a practical target classification problem using a single-pixel camera that directly acquires compressive image projections, we achieve high classification rates using many fewer measurements than the dimensionality of the images.

The new theory of compressive sensing enables direct analog-to-information conversion of compressible signals at sub-Nyquist acquisition rates. The authors develop new theory, algorithms, performance bounds, and a prototype implementation for an analog-to-information converter based on random demodulation. The architecture is particularly apropos for wideband signals that are sparse in the time-frequency plane. End-to-end simulations of a complete transistor-level implementation prove the concept under the effect of circuit nonidealities.

Compressive sensing is an emerging field based on the rev elation that a small group of non-adaptive linear projections of a compressible signal contains enough information for reconstruction and processing. In this paper, we propose algorithms and hardware to support a new theory of compressive imaging. Our approach is based on a new digital image/video camera that directly acquires random projections of the signal without first collecting the pixels/voxels. Our camera architecture employs a digital micromirror array to perform optical calculations of linear projections of an image onto pseudorandom binary patterns. Its hallmarks include the ability to obtain an image with a single detection element while measuring the image/video fewer times than the number of pixels this can significantly reduce the computation required for video acquisition/encoding. Because our system relies on a single photon detector, it can also be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers. We are currently testing a proto type design for the camera and include experimental results.