Browsing by Author "Laska, Jason N."

Now showing 1 - 12 of 12
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    Democracy in action: Quantization, saturation, and compressive sensing
    (2010) Laska, Jason N.; Baraniuk, Richard G.
    We explore and exploit a heretofore relatively unexplored hallmark of compressive sensing (CS), the fact that certain CS measurement systems are democratic, which means that each measurement carries roughly the same amount of information about the signal being acquired. Using this property, we re-think how to quantize the compressive measurements. In Shannon-Nyquist sampling, we scale down the analog signal amplitude (and therefore increase the quantization error) to avoid the gross saturation errors. In stark contrast, we demonstrate a CS system achieves the best performance when we operate at a significantly nonzero saturation rate. We develop two methods to recover signals from saturated CS measurements. The first directly exploits the democracy property by simply discarding the saturated measurements. The second integrates saturated measurements as constraints into standard linear programming and greedy recovery techniques. Finally, we develop a simple automatic gain control system that uses the saturation rate to optimize the input gain.
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    Method and apparatus for automatic gain control for nonzero saturation rates
    (2013-07-16) Baraniuk, Richard G.; Laska, Jason N.; Boufounos, Petros T.; Davenport, Mark A.; Rice University; United States Patent and Trademark Office
    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.
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    Method and apparatus for compressive imaging device
    (2014-09-30) Baraniuk, Richard G.; Baron, Dror Z.; Duarte, Marco F.; Kelly, Kevin F.; Lane, Courtney C.; Laska, Jason N.; Takhar, Dharmpal; Wakin, Michael B.; Rice University; United States Patent and Trademark Office
    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—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.
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    Method and apparatus for compressive imaging device
    (2012-06-12) Baraniuk, Richard G.; Baron, Dror Z.; Duarte, Marco F.; Kelly, Kevin F.; Lane, Courtney C.; Laska, Jason N.; Takhar, Dharmpal; Wakin, Michael B.; Rice University; United States Patent and Trademark Office
    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—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.
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    Method and apparatus for compressive parameter estimation and tracking
    (2013-10-22) Baraniuk, Richard G.; Boufounos, Petros T.; Schnelle, Stephen R.; Davenport, Mark A.; Laska, Jason N.; Rice University; United States Patent and Trademark Office
    A method for estimating and tracking locally oscillating signals. The method comprises the steps of taking measurements of an input signal that approximately preserve the inner products among signals in a class of signals of interest and computing an estimate of parameters of the input signal from its inner products with other signals. The step of taking measurements may be linear and approximately preserve inner products, or may be non-linear and approximately preserves inner products. Further, the step of taking measurements is nonadaptive and may comprise compressive sensing. In turn, the compressive sensing may comprise projection using one of a random matrix, a pseudorandom matrix, a sparse matrix and a code matrix. The step of tracking said signal of interest with a phase-locked loop may comprise, for example, operating on compressively sampled data or by operating on compressively sampled frequency modulated data, tracking phase and frequency.
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    Method and apparatus for on-line compressed sensing
    (2014-04-01) Baraniuk, Richard G.; Baron, Dror Z.; Duarte, Marco F.; Elnozahi, Mohamed; Wakin, Michael B.; Davenport, Mark A.; Laska, Jason N.; Tropp, Joel A.; Massoud, Yehia; Kirolos, Sami; Ragheb, Tamer; Rice University; United States Patent and Trademark Office
    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 bottleneck 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.
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    Method and apparatus for signal reconstruction from saturated measurements
    (2013-06-04) Baraniuk, Richard G.; Laska, Jason N.; Boufounos, Petros T.; Davenport, Mark A.; Rice University; United States Patent and Trademark Office
    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.
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    Multiscale random projections for compressive classification
    (2007-09-01) Duarte, Marco F.; Davenport, Mark A.; Wakin, Michael B.; Laska, Jason N.; Takhar, Dharmpal; Kelly, Kevin F.; Baraniuk, Richard G.
    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.
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    Regime Change: Sampling Rate vs. Bit-Depth in Compressive Sensing
    (2012) Laska, Jason N.; Baraniuk, Richard G.
    The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement compression (MC) regime, a high SNR favors acquiring fewer measurements with more bits per measurement (as in conventional CS); in the quantization compression (QC) regime, a low SNR favors acquiring more measurements with fewer bits per measurement (as in this thesis). A surprise from our analysis and experiments is that in many practical applications it is better to operate in the QC regime, even acquiring as few as 1 bit per measurement. The above philosophy extends further to practical CS ADC system designs. We propose two new CS architectures, one of which takes advantage of the fact that the sampling and quantization operations are performed by two different hardware components. The former can be employed at high rates with minimal costs while the latter cannot. Thus, we develop a system that discretizes in time, performs CS preconditioning techniques, and then quantizes at a low rate.
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    Single-pixel imaging via compressive sampling
    (2008-03-01) Duarte, Marco F.; Davenport, Mark A.; Takhar, Dharmpal; Laska, Jason N.; Sun, Ting; Kelly, Kevin F.; Baraniuk, Richard G.
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    The smashed filter for compressive classification and target recognition
    (2007-01-01) Davenport, Mark A.; Duarte, Marco F.; Wakin, Michael B.; Laska, Jason N.; Takhar, Dharmpal; Kelly, Kevin F.; Baraniuk, Richard G.
    The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible image or signal from a small set of linear, non-adaptive (even random) projections. However, in many applications, including object and target recognition, we are ultimately interested in making a decision about an image rather than computing a reconstruction. We propose here a framework for compressive classification that operates directly on the compressive measurements without first reconstructing the image. We dub the resulting dimensionally reduced matched filter the smashed filter. The first part of the theory maps traditional maximum likelihood hypothesis testing into the compressive domain; we find that the number of measurements required for a given classification performance level does not depend on the sparsity or compressibility of the images but only on the noise level. The second part of the theory applies the generalized maximum likelihood method to deal with unknown transformations such as the translation, scale, or viewing angle of a target object. We exploit the fact the set of transformed images forms a low-dimensional, nonlinear manifold in the high-dimensional image space. We find that the number of measurements required for a given classification performance level grows linearly in the dimensionality of the manifold but only logarithmically in the number of pixels/samples and image classes. Using both simulations and measurements from a new single-pixel compressive camera, we demonstrate the effectiveness of the smashed filter for target classification using very few measurements.
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    Trust, But Verify: Fast and Accurate Signal Recovery from 1-bit Compressive Measurements
    (2010-11) Laska, Jason N.; Wen, Zaiwen; Yin, Wotao; Baraniuk, Richard G.
    The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross non-linearities applied to the measurements. In this paper we introduce a new algorithm --restricted-step shrinkage (RSS) -- to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for non-convex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest.