William Marsh Rice University

Michael B Wakin

Richard G Baraniuk

Marco F Duarte

Dror Z Baron

Mark A Davenport

Jason N Laska

Courtney C Lane

Kevin F Kelly

Shriram Sarvotham

Dharmpal Takhar

Mohamed Elnozahi

Joel A Tropp

Yehia Massoud

Sami Kirolos

Tamer Ragheb

Kevin F Kelley

Ilan N Goodman

A new digital image/video camera that directly acquires random projections of the incident light field without first collecting the pixels/voxels. In one preferred embodiment, the camera 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 only a single detection element while measuring the image/video fewer times than the number of pixels or voxels&#x2014;this can significantly reduce the computation required for image/video acquisition/encoding. Since the system features a single photon detector, it can also be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers.

Method and apparatus for compressive imaging device

A typical data acquisition system takes periodic samples of a signal, image, or other data, often at the so-called Nyquist/Shannon sampling rate of two times the data bandwidth in order to ensure that no information is lost. In applications involving wideband signals, the Nyquist/Shannon sampling rate is very high, even though the signals may have a simple underlying structure. Recent developments in mathematics and signal processing have uncovered a solution to this Nyquist/Shannon sampling rate bottlenck for signals that are sparse or compressible in some representation. We demonstrate and reduce to practice methods to extract information directly from an analog or digital signal based on altering our notion of sampling to replace uniform time samples with more general linear functionals. One embodiment of our invention is a low-rate analog-to-information converter that can replace the high-rate analog-to-digital converter in certain applications involving wideband signals. Another embodiment is an encoding scheme for wideband discrete-time signals that condenses their information content.

Method and apparatus for on-line compressed sensing

The recently introduced theory of Compressive Sensing (CS) enables a new method for signal recovery from incomplete information (a reduced set of 'compressive' linear measurements), based on the assumption that the signal is sparse in some dictionary. Such compressive measurement schemes are desirable in practice for reducing the costs of signal acquisition, storage, and processing. However, the current CS framework considers only a certain task (signal recovery) and only in a certain model setting (sparsity). We show that compressive measurements are in fact information scalable, allowing one to answer a broad spectrum of questions about a signal when provided only with a reduced set of compressive measurements. These questions range from complete signal recovery at one extreme down to a simple binary detection decision at the other. (Questions in between include, for example, estimation and classification.) We provide techniques such as a 'compressive matched filter' for answering several of these questions given the available measurements, often without needing to first reconstruct the signal. In many cases, these techniques can succeed with far fewer measurements than would be required for full signal recovery, and such techniques can also be computationally more efficient. Based on additional mathematical insight, we discuss information scalable algorithms in several model settings, including sparsity (as in CS), but also in parametric or manifold-based settings and in model-free settings for generic statements of detection, classification, and estimation problems.

Method and apparatus for signal detection, classification and estimation from compressive measurements

A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xof said plurality of digital signals or images an innovative component xof each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement y, where ycomprises a vector with only nentries, where nis less than m, making a measurement yfor each of said correlated digital signals, where ycomprises a vector with only nentries, where nis less than m, and from each said innovation components y, producing an approximate reconstruction of each m-vector xusing said common component yand said innovative component y.

Method and apparatus for distributed compressed sensing

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Castle Rock, CO, United States of America

Michael B Wakin