scispace - formally typeset
Search or ask a question
Author

Jason N. Laska

Bio: Jason N. Laska is an academic researcher from Rice University. The author has contributed to research in topics: Compressed sensing & Signal. The author has an hindex of 27, co-authored 41 publications receiving 9515 citations. Previous affiliations of Jason N. Laska include BAE Systems & University of Illinois at Urbana–Champaign.

Papers
More filters
Journal ArticleDOI
TL;DR: A new camera architecture based on a digital micromirror device with the new mathematical theory and algorithms of compressive sampling is presented that can operate efficiently across a broader spectral range than conventional silicon-based cameras.
Abstract: In this article, the authors present a new approach to building simpler, smaller, and cheaper digital cameras that can operate efficiently across a broader spectral range than conventional silicon-based cameras. The approach fuses a new camera architecture based on a digital micromirror device with the new mathematical theory and algorithms of compressive sampling.

3,316 citations

Journal ArticleDOI
TL;DR: A new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components that supports the empirical observations, and a detailed theoretical analysis of the system's performance is provided.
Abstract: 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.

1,138 citations

Journal ArticleDOI
TL;DR: This paper investigates an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement, and introduces the binary iterative hard thresholding algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.
Abstract: 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 e-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.

645 citations

Proceedings ArticleDOI
TL;DR: A new camera architecture is developed that employs a digital micromirror array to perform optical calculations of linear projections of an image onto pseudorandom binary patterns that can be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers.
Abstract: Compressive Sensingis an emerging field based on the revelation that a small numbe r of linear projections of a compressible signal contain enough information for reconstruction and processing. It has many promising implications and enables the design of new kinds of Compressive Imagingsystems and cameras. In this paper, we develop a new camera architecture that 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 obtai n an image with a single detection element while sampling the image fewer times than the number of pixels. Other attractive properties include its universality, robustness, scalab ility, progressivity, and computational asymmetry. The most intriguing feature of the system is that, since it relies on a sing le photon detector, it can be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers.

644 citations

Proceedings ArticleDOI
27 May 2007
TL;DR: The new theory of compressive sensing enables direct analog-to-information conversion of compressible signals at sub-Nyquist acquisition rates and proves the concept under the effect of circuit nonidealities.
Abstract: 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.

467 citations


Cited by
More filters
Journal ArticleDOI
TL;DR: A new iterative recovery algorithm called CoSaMP is described that delivers the same guarantees as the best optimization-based approaches and offers rigorous bounds on computational cost and storage.

3,970 citations

Journal ArticleDOI
TL;DR: This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate, called compressive sensing, which employs nonadaptive linear projections that preserve the structure of the signal.
Abstract: This lecture note presents a new method to capture and represent compressible signals at a rate significantly below the Nyquist rate. This method, called compressive sensing, employs nonadaptive linear projections that preserve the structure of the signal; the signal is then reconstructed from these projections using an optimization process.

3,555 citations

Journal ArticleDOI
TL;DR: In many important statistical applications, the number of variables or parameters p is much larger than the total number of observations n as discussed by the authors, and it is possible to estimate β reliably based on the noisy data y.
Abstract: In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y=Xβ+z, where β∈Rp is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n≪p, and the zi’s are i.i.d. N(0, σ^2). Is it possible to estimate β reliably based on the noisy data y?

3,539 citations

Journal ArticleDOI
TL;DR: It is shown that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum-rank solution can be recovered by solving a convex optimization problem, namely, the minimization of the nuclear norm over the given affine space.
Abstract: The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NP-hard because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum-rank solution can be recovered by solving a convex optimization problem, namely, the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability, provided the codimension of the subspace is sufficiently large. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this preexisting concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization. We also discuss several algorithmic approaches to minimizing the nuclear norm and illustrate our results with numerical examples.

3,432 citations

Journal ArticleDOI
TL;DR: A new camera architecture based on a digital micromirror device with the new mathematical theory and algorithms of compressive sampling is presented that can operate efficiently across a broader spectral range than conventional silicon-based cameras.
Abstract: In this article, the authors present a new approach to building simpler, smaller, and cheaper digital cameras that can operate efficiently across a broader spectral range than conventional silicon-based cameras. The approach fuses a new camera architecture based on a digital micromirror device with the new mathematical theory and algorithms of compressive sampling.

3,316 citations