Abstract: A signal x is reconstructed by measuring the signal x as a vector y of measurements yi, wherein the measurements yi are distorted, and each measurement yi has an associated value. The measurements yi in the vector y are ordered according to the associated values, wherein each sorted measurement has an index corresponding to the ordering to form an ordered index sequence. Then, a reconstruction method is applied to the ordered index sequence to produce an estimate {circumflex over (X)} of the signal x.

Abstract: A signal x is reconstructed from sparse sign measurements y. Estimated measurements {tilde over (y)} are obtained from a previous estimate {circumflex over (x)}l?1 and a measurement matrix ? according to {tilde over (y)}l=?{circumflex over (x)}l?1. A correction signal is applied to inconsistent measurements, so that consistent reconstruction can be performed.

Abstract: A method reconstructs a streaming signal xn from streaming measurements by maintaining a working set of measurements, a working snapshot of the measurement system, an internal working signal estimate, and an external working signal estimate. Using a current working set of measurements, the internal working signal estimates, the working snapshot of the measurement system, and a model of a signal sparsity are refined. The external working signal estimate is refreshed. A subset of coefficients of the external working signal estimate is committed to an output. A next streaming measurement and a corresponding next measurement vector are received. The working set of measurements, the working snapshot of the measurement system, and the internal working signal estimate are updated to incorporate the next measurement and the corresponding measurement vector. Then, an oldest measurement and a corresponding oldest measurement vector, and an effect of the committed subset of coefficients are removed.

Abstract: An encoded signal is decoded based on statistical dependencies between the encoded signal and the side information. A statistical reliability of each transform block of the side information is determined as a function of absolute values of transform coefficients of a transform block. The transform blocks of the side information are grouped into a set of groups based on the statistical reliability of each transform block. The decoding is performed using a statistical dependency between a transform block of the encoded signal and a group including a corresponding transform block of the side information.

Abstract: Pulses are transmitted into a scene by an array of the transducers, wherein each pulse has wideband ultrasound frequency, wherein the pulses are transmitted simultaneously, and wherein a pattern of the wideband ultrasound frequencies in each pulse is unique with respect to the patterns of each other pulse. The pulses as received when the pulse are reflected by the scene and objects in the scene. Each received pulse is sampled and decomposed using a Fourier transform to produce frequency coefficients, which are stacked to produce a linear system modeling a reflectivity of the scene and the objects. Then, a recovery method is applied to the linear system to recover the reflectivity of the scene and the objects.

Abstract: A method for compressive domain filtering and interference cancelation processes compressive measurements to eliminate or attenuate interference while preserving the information or geometry of the set of possible signals of interest. A signal processing apparatus assumes that the interfering signal lives in or near a known subspace that is partially or substantially orthogonal to the signal of interest, and then projects the compressive measurements into an orthogonal subspace and thus eliminate or attenuate the interference. This apparatus yields a modified set of measurements that can provide a stable embedding of the set of signals of interest, in which case it is guaranteed that the processed measurements retain sufficient information to enable the direct recovery of this signal of interest, or alternatively to enable the use of efficient compressive-domain algorithms for further processing.

Abstract: A method for recovering a signal by measuring the signal to produce a plurality of compressive sensing measurements, discarding saturated measurements from the plurality of compressive sensing measurements and reconstructing the signal from remaining measurements from the plurality of compressive sensing measurements. Alternatively, a method for recovering a signal comprising the steps of measuring a signal to produce a plurality of compressive sensing measurements, identifying saturated measurements in the plurality of compressive sensing measurements and reconstructing the signal from the plurality of compressive sensing measurements, wherein the recovered signal is constrained such that magnitudes of values corresponding to the identified saturated measurements are greater than a predetermined value.

Abstract: A method for automatic gain control comprising the steps of measuring a signal using compressed sensing to produce a sequence of blocks of measurements, applying a gain to one of the blocks of measurements, adjusting the gain based upon a deviation of a saturation rate of the one of the blocks of measurements from a predetermined nonzero saturation rate and applying the adjusted gain to a second of the blocks of measurements. Alternatively, a method for automatic gain control comprising the steps of applying a gain to a signal, computing a saturation rate of the signal and adjusting the gain based upon a difference between the saturation rate of the signal and a predetermined nonzero saturation rate.

Abstract: A method reconstructs a streaming signal xn from streaming measurements by maintaining a working set of measurements, a working snapshot of the measurement system, an internal working signal estimate, and an external working signal estimate. Using a current working set of measurements, the internal working signal estimates, the working snapshot of the measurement system, and a model of a signal sparsity are refined. The external working signal estimate is refreshed. A subset of coefficients of the external working signal estimate is committed to an output. A next streaming measurement and a corresponding next measurement vector are received. The working set of measurements, the working snapshot of the measurement system, and the internal working signal estimate are updated to incorporate the next measurement and the corresponding measurement vector. Then, an oldest measurement and a corresponding oldest measurement vector, and an effect of the committed subset of coefficients are removed.

Abstract: A signal x is reconstructed by measuring the signal x as a vector y of measurements yi, wherein the measurements yi are distorted, and each measurement yi has an associated value. The measurements yi in the vector y are ordered according to the associated values, wherein each sorted measurement has an index corresponding to the ordering to form an ordered index sequence. Then, a reconstruction method is applied to the ordered index sequence to produce an estimate {circumflex over (X)} of the signal x.

Abstract: A signal x is reconstructed from sparse sign measurements y. Estimated measurements {tilde over (y)} are obtained from a previous estimate xl-1 and a measurement matrix ? according to {tilde over (y)}l=? xl-1. A correction signal is applied to inconsistent measurements, so that consistent reconstruction can be performed.

Abstract: We have developed a new method and apparatus for tracking and estimating parameters of locally oscillating signals from measurements that approximately preserve the inner product among signals in a class of signals of interest. Random demodulation, random sampling, and coset sampling are three prime examples of these techniques. One example of this is a compressive phase locked loops (PLL), which has a wide variety of applications, including but not limited to communications, phase tracking, robust control, sensing, and frequency modulation (FM) demodulation. The design modifies classical PLL designs to operate with CS-based sampling systems. By introducing a compressive sampler at the output of the oscillator and by appropriately adjusting the phase difference estimator we enable the use of PLLs with modern CS sampling technology. Other modifications can be made to reduce concerns such as normalization of the measurements, for example using the QCS-PLL.