Humans are visual animals, and imaging sensors that extend our reach – cameras – have improved dramatically in recent times thanks to the introduction of CCD and CMOS digital technology. Consumer digital cameras in the mega-pixel range are now ubiquitous thanks to the happy coincidence that the semiconductor material of choice for large-scale electronics integration (silicon) also happens to readily convert photons at visual wavelengths into electrons. On the contrary, imaging at wavelengths where silicon is blind is considerably more complicated, bulky, and expensive. Thus, for comparable resolution, a $500 digital camera for the visible becomes a $50,000 camera for the infrared. In this paper, we present a new approach to building simpler, smaller, and cheaper digital cameras that can operate efficiently across a much broader spectral range than conventional silicon-based cameras. Our approach fuses a new camera architecture based on a digital mi-cromirror device (DMD – see Sidebar: Spatial Light Modulators) with the new mathematical theory and algorithms of compressive sampling (CS – see Sidebar: Compressive Sampling in a Nutshell). CS combines sampling and compression into a single nonadaptive linear measurement process [1–4]. Rather than measuring pixel samples of the scene under view, we measure inner products

Compressive Sensing is an emerging field based on the revelation that a small number 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 Imaging systems 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 obtain 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, scalability, progressivity, and computational asymmetry. The most intriguing feature of the system is that, since it relies on a single photon detector, it can be adapted to image at wavelengths that are currently impossible with conventional CCD and CMOS imagers.

Compressive Sensing is an emerging field based on the revelation 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 prototype design for the camera and include experimental results.

Abstract. Compressive Sensing is an emerging field based on the revelation that a small group of nonadaptive 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 light field 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/voxels; this can significantly reduce the computation required for video acquisition/encoding. Since 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 prototype design for the camera and include experimental results. Index Terms: camera, compressive sensing, imaging, incoherent projections, linear programming, random

Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices, we develop a tensor-based extension of the matrix CUR decomposition. The tensor-CUR decomposition is most relevant as a data analysis tool when the data consist of one mode that is qualitatively different from the others. In this case, the tensor-CUR decomposition approximately expresses the original data tensor in terms of a basis consisting of underlying subtensors that are actual data elements and thus that have a natural interpretation in terms of the processes generating the data. Assume the data may be modeled as a (2+1)-tensor, i.e., an m×n×p tensor A in which the first two modes are similar and the third is qualitatively different. We refer to each of the p different m × n matrices as “slabs ” and each of the mn different p-vectors as “fibers.” In this case, the tensor-CUR algorithm computes an approximation to the data tensor A that is of the form CUR, where C is an m×n×c tensor consisting of a small number c of the slabs, R is an r × p matrix consisting of a small number r of the fibers, and U is an appropriately defined and easily computed c × r encoding matrix. Both C and R may be chosen by randomly sampling either slabs or fibers according to a judiciously chosen and data-dependent probability distribution, and both c and r depend on a rank parameter k, an error parameter ɛ, and a failure probability δ. Under

The human ability to recognize, identify and compare sounds based on their approximation of particular vowels provides an intuitive, easily learned representation for complex data. We describe implementations of vocal tract models specifically designed for sonification purposes. The models described are based on classical models including Klatt[1] and Cook[2]. Implementation of these models in MatLab, STK[3], and PD[4] is presented. Various sonification methods were tested and evaluated using data sets of hyperspectral images of colon cells 1   2. 1.

Humans are visual animals, and imaging sensors that extend our reach— cameras—have improved dramatically in recent times thanks to the introduction of CCD and CMOS digital technology. Consumer digital cameras in the megapixel range are now ubiquitous thanks to the happy coincidence that the semiconductor material of choice for large-scale electronics integration (silicon) also happens to readily convert photons at visual wavelengths into electrons. On the contrary, imaging at wavelengths where silicon is blind is considerably more complicated, bulky, and expensive. Thus, for comparable resolution, a US$500 digital camera for the visible becomes a US$50,000 camera for the infrared. In this article, we present a new approach to building simpler, smaller, and cheaper digital cameras that can operate efficiently across a much broader spectral range than conventional silicon-based cameras. Our approach fuses a new camera architecture Digital Object Identifier 10.1109/MSP.2007.914730 1053-5888/08/$25.00©2008IEEE IEEE SIGNAL PROCESSING MAGAZINE [83] MARCH 2008based on a digital micromirror device (DMD—see “Spatial Light Modulators”) with the new mathematical theory and algorithms of compressive sampling (CS—see “CS in a Nutshell”). CS combines sampling and compression into a single nonadaptive linear measurement process [1]–[4]. Rather than measuring pixel samples of the scene under view, we measure inner products between the scene and a set of test functions. Interestingly, random test functions play a key role, making each measurement a random sum of pixel values taken across the entire image. When the scene under view is compressible by an algorithm like JPEG or JPEG2000, the CS theory enables us to stably reconstruct an image of the scene from fewer measurements than the number of reconstructed pixels. In this manner we achieve sub-Nyquist image acquisition.

Humans are visual animals, and imaging sensors that extend our reach – cameras – have improved dramatically in recent times thanks to the introduction of CCD and CMOS digital technology. Consumer digital cameras in the mega-pixel range are now ubiquitous thanks to the happy coincidence that the semiconductor material of choice for large-scale electronics integration (silicon) also happens to readily convert photons at visual wavelengths into electrons. On the contrary, imaging at wavelengths where silicon is blind is considerably more complicated, bulky, and expensive. Thus, for comparable resolution, a $500 digital camera for the visible becomes a $50,000 camera for the infrared. In this paper, we present a new approach to building simpler, smaller, and cheaper digital cameras that can operate efficiently across a much broader spectral range than conventional silicon-based cameras. Our approach fuses a new camera architecture based on a digital micromirror device (DMD – see Sidebar: Spatial Light Modulators) with the new mathematical theory and algorithms of compressive sampling (CS – see Sidebar: Compressive Sampling in a Nutshell). CS combines sampling and compression into a single nonadaptive linear measurement process [1–4]. Rather than measuring pixel samples of the scene under view, we measure inner products

Abstract—This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this setting, standard CS techniques cannot be applied directly for several reasons. First, the usual signal-independent and/or bounded noise models do not apply to Poisson noise, which is nonadditive and signal-dependent. Second, the CS matrices typically considered are not feasible in real optical systems because they do not adhere to important constraints, such as nonnegativity and photon flux preservation. Third, the typical `2 0 `1 minimization leads to overfitting in the high-intensity regions and oversmoothing in the low-intensity areas. In this paper, we describe how a feasible positivity-and flux-preserving sensing matrix can be constructed, and then analyze the performance of a CS reconstruction approach for Poisson data that minimizes an objective function consisting of a negative Poisson log likelihood term and a penalty term which measures signal sparsity. We show that, as the overall intensity of the underlying signal increases, an upper bound on the reconstruction error decays at an appropriate rate (depending on the compressibility of the signal), but that for a fixed signal intensity, the error bound actually grows with the number of measurements or sensors. This surprising fact is both proved theoretically and justified based on physical intuition. Index Terms—Complexity regularization, compressive sampling, nonparametric estimation, photon-limited imaging, sparsity. I.

Abstract—This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known spectral targets and spectral anomalies from few projection measurements of spectral images. The proposed approaches accommodate spectra of different signal strengths contaminated by a colored Gaussian background, and perform detection without reconstructing the spectral image from the observations. The theoretical performance bounds of the target detector highlight fundamental tradeoffs among the number of measurements collected, amount of background signal present, signal-to-noise ratio, and similarity among potential targets in a known spectral dictionary. The anomaly detector is designed to control the number of false discoveries below a desired level and can be adapted to uncertainties in the user’s knowledge of the spectral dictionary. Unlike approaches based on the principles of compressed sensing, the proposed approach does not depend on a known sparse representation of targets; rather, the theoretical performance bounds exploit the structure of a known dictionary of targets and the distance preservation property of the measurement matrix. Simulation experiments illustrate the practicality and effectiveness of the proposed approaches.