KEYWORDS: Error analysis, Field programmable gate arrays, Signal processing, Image processing, Data processing, Bessel functions, Computer engineering, 3D image processing, 3D modeling, Model-based design
This paper presents a systematic approach for automatic generation of look-up-table (LUT) for function evaluations and minimization in hardware resource on field programmable gate arrays (FPGAs). The class of functions supported by this approach includes sine, cosine, exponentials, Gaussians, the central B-splines, and certain cylinder functions that are frequently used in applications for signal and image processing and data processing. In order to meet customer requirements in accuracy and speed as well as constraints on the use of area and on-chip memory, the function evaluation is based on numerical approximation with Taylor polynomials. Customized data precisions are supported in both fixed point and floating point representations. The optimization procedure involves a search in three-dimensional design space of data precision, sampling density and approximation degree. It utilizes both model-based estimates and gradient-based information gathered during the search. The approach was tested with actual synthesis results on the Xilinx Virtex-2Pro FPGA platform.
This paper presents an acceleration method, using both algorithmic and architectural means, for fast calculation
of local correlation coefficients, which is a basic image-based information processing step for template or
pattern matching, image registration, motion or change detection and estimation, compensation of changes, or
compression of representations, among other information processing objectives. For real-time applications, the
complexity in arithmetic operations as well as in programming and memory access latency had been a divisive
issue between the so-called correction-based methods and the Fourier domain methods. In the presented
method, the complexity in calculating local correlation coefficients is reduced via equivalent reformulation that
leads to efficient array operations or enables the use of multi-dimensional fast Fourier transforms, without
losing or sacrificing local and non-linear changes or characteristics.
KEYWORDS: Video, Cameras, Video surveillance, Reconstruction algorithms, Video compression, Image compression, Image resolution, Sensors, Video processing, Imaging systems
With this work we propose spatio-temporal sampling strategies for video using a lenslet array computational imaging system and explore the opportunities and challenges in the design of compressive video sensors and corresponding processing algorithms. The redundancies in video streams are exploited by (a) sampling the sub-apertures of a multichannel (TOMBO) camera, and (b) by the computational reconstruction to achieve low power and low complexity video sensors. A spatial and a spatio-temporal sampling strategy are considered, taking into account the feasibility for implementation in the focal-plane readout hardware. The algorithms used to reconstruct the video frames from measurements are also presented.
This paper describes numerical estimation techniques for coded aperture snapshot spectral imagers (CASSI). In
a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation
of both spectral information and 2D spatial information of a scene. The spatial information is modulated by
a coded aperture and the spectral information is modulated by a dispersive element. The estimation process
decodes the 2D measurements to render a three-dimensional spatio-spectral estimate of the scene, and is therefore
an indispensable component of the spectral imager. Numerical estimation results are presented.
We address the discrepancy that existed between the low arithmetic complexity of nonuniform Fast Fourier Transform (NUFFT) algorithms and high latency in practical use of NUFFTs with large data sets, especially, in multi-dimensional domains. The execution time of a NUFFT can be longer by a factor of two orders of magnitude
than what is expected by the arithmetic complexity. We examine the architectural factors in the latency, primarily on the non-even latency distribution in memory references across different levels in the memory hierarchy. We then introduce an effective approach to reducing the latency substantially by exploiting the geometric features in the sample translation stage and making memory references local. The restructured NUFFT algorithms render efficient computation in sequential as well as in parallel. Experimental results and improvements for radially encoded magnetic resonance image reconstruction are presented.
This paper presents an acceleration method, using both algorithmic and architectural means, for fast calculation of local correlation coefficients, which is a basic image-based information processing step for template or pattern matching, image registration, motion or change detection and estimation, compensation of changes, or compression of representations, among other information processing objectives. For real-time applications, the complexity in arithmetic operations as well as in programming and memory access latency had been a divisive issue between the so-called correction-based methods and the Fourier domain methods. In the presented method, the complexity in calculating local correlation coefficients is reduced via equivalent reformulation that leads to efficient array operations or enables the use of multi-dimensional fast Fourier transforms, without losing or sacrificing local and non-linear changes or characteristics. The computation time is further reduced by utilizing modern multi-core architectures, such as the Sony-Toshiba-IBM Cell processor, with high processing speed and low power consumption.
This paper introduces the theoretical development of a numerical method, named NeAREst, for solving non-negative
linear inverse problems, which arise often from physical or probabilistic models, especially, in image
estimation with limited and indirect measurements. The Richardson-Lucy (RL) iteration is omnipresent in
conventional methods that are based on probabilistic assumptions, arguments and techniques. Without resorting
to probabilistic assumptions, NeAREst retains many appealing properties of the RL iteration by utilizing it as
the substrate process and provides much needed mechanisms for acceleration as well as for selection of a target
solution when many admissible ones exist.
We consider compressive sensing in the context of optical spectroscopy. With compressive sensing, the ratio between the number of measurements and the number of estimated values is less than one, without compromising the fidelity in estimation. A compressive sensing system is composed of a measurement subsystem that maps a
signal to digital data and an inference algorithm that maps the data to a signal estimate. The inference algorithm exploits both the information captured in the measurement and certain a priori information about the signals of interest, while the measurement subsystem provides complementary, signal-specific information at the lowest sampling rate possible. Codesign of the measurement strategies, the model of a priori information, and the
inference algorithm is the central problem of system design. This paper describes measurement constraints specific to optical spectrometers, inference models based on physical or statistical characteristics of the signals, as well as linear and nonlinear reconstruction algorithms. We compare the fidelity of sampling and inference strategies over a family of spectral signals.
This paper describes a compressive sensing strategy developed under the Compressive Optical MONTAGE Photography Initiative. Multiplex and multi-channel measurements are generally necessary for compressive sensing. In a compressive imaging system described here, static focal plane coding is used with multiple image apertures for non-degenerate multiplexing and multiple channel sampling. According to classical analysis, one might expect the number of pixels in a reconstructed image to equal the total number of pixels across the sampling channels, but we demonstrate that the system can achieve up to 50% compression with conventional benchmarking images. In general, the compression rate depends on the compression potential of an image with respect to the coding and decoding schemes employed in the system.
We have designed and constructed a multimodal multiplex Raman spectrometer which uses multi-wavelength excitation to better detect signals in the presence of fluorescence by taking advantage of the shift-variance of the Raman signal with respect to excitation frequency. Coupled with partial-least-squares (PLS) regression, the
technique applied to ethanol estimation in a tissue phantom achieves root-mean-squared-cross-validation errors (RMSCVE) of 9.2 mmol/L with a model formed with 2 principal components, compared to a single wavelength data set with equivalent energy where 7 principal components were used to achieve an RMSCVE of 39.1 mmol/L.
With this work we show the use of focal plane coding to produce nondegenerate data between subapertures of an imaging system. Subaperture data is integrated to form a single high resolution image. Multiple apertures generate multiple copies of a scene on the detector plane. Placed in the image plane, the focal plane mask applies a unique code to each of these sub-images. Within each sub-image, each pixel is masked so that light from only certain optical pixels reaches the detector. Thus, each sub-image measures a different linear combination of optical pixels. Image reconstruction is achieved by inversion of the transformation performed by the imaging system. Registered detector pixels in each sub-image represent the magnitude of the projection of the same optical information onto different sampling vectors. Without a coding element, the imaging system would be limited by the spatial frequency response of the electronic detector pixel. The small mask features allow the imager to broaden this response and reconstruct higher spatial frequencies than a conventional coarsely sampling focal plane.
The Compressive Optical MONTAGE Photography Initiative (COMP-I) is an initiative under DARPA's MONTAGE program. The goals of COMP-I are to produce 1 mm thick visible imaging systems and 5 mm thick IR systems without compromising pixel-limited resolution. Innovations of COMP-I include focal-plane coding, block-wise focal plane codes, birefringent, holographic and 3D optical elements for focal plane remapping and embedded algorithms for image formation. In addition to meeting MONTAGE specifications for sensor thickness, focal plane coding enables a reduction in the transverse aperture size, physical layer compression of multispectral and hyperspectral data cubes, joint optical and electronic optimization for 3D sensing, tracking, feature-specific imaging and conformal array deployment.
Optical diagnostics in biological materials are hindered by fluorescence and scattering. We have developed a multimodal, multiplex, coded-aperture Raman spectrometer to detect alcohol in a lipid tissue phantom solution.
We introduce a novel approach for compressive coding at the sensor layer for an integrated imaging system. Compression at the physical layer reduces the measurements-to-pixels ratio and the data volume for storage and transmission, without confounding image estimation or analysis. We introduce a particular compressive coding scheme based on the quantized Cosine transform (QCT) and the corresponding image reconstruction scheme. The QCT is restricted on the ternary set {-1,0,1} for economic implementation with a focal plane optical pixel mask. Combined with the reconstruction scheme, the QCT-based coding is shown favorable over existing coding schemes from the coded aperture literature, in terms of both reconstruction quality and photon efficiency.
KEYWORDS: Digital signal processing, Signal processing, Data communications, Fourier transforms, Matrices, Parallel computing, Array processing, Image processing, Algorithm development, Telecommunications
We present a high performance implementation of the FFT algorithm on the BOPS ManArray parallel DSP processor. The ManArray we consider for this application consists of an array controller and 2 to 4 fully interconnected processing elements. To expose the parallelism inherent to an FFT algorithm we use a factorization of the DFT matrix in Kronecker products, permutation and diagonal matrices. Our implementation utilizes the multiple levels of parallelism that are available on the ManArray. We use the special multiply complex instruction, that calculates the product of two complex 32-bit fixed point numbers in 2 cycles (pipelinable). Instruction level parallelism is exploited via the indirect Very Long Instruction Word (iVLIW). With an iVLIW, in the same cycle a complex number is read from memory, another complex number is written to memory, a complex multiplication starts and another finishes, two complex additions or subtractions are done and a complex number is exchanged with another processing element. Multiple local FFTs are executed in Single Instruction Multiple Data (SIMD) mode, and to avoid a costly data transposition we execute distributed FFTs in Synchronous Multiple Instructions Multiple Data (SMIMD) mode.
Real-time adaptive-optics is a means for enhancing the resolution of ground based, optical telescopes beyond the limits previously imposed by the turbulent atmosphere. One approach for linear performance modeling of closed-loop adaptive-optics system involves calculating very large covariance matrices whose components can be represented by sums of Hankel transform based integrals. In this paper we investigate approximate matrix factorizations of discretizations of such integrals. Two different approximate factorizations based upon representations of the underlying Bessel function are given, the first using a series representation due to Ellerbroek and the second an integral representations. The factorizations enable fast methods for both computing and applying the covariance matrices. For example, in the case of an equally spaced grid, it is shown that applying the approximated covariance matrix to a vector can be accomplished using the derived integral-based factorization involving a 2D fast cosine transform and a 2D separable fast multiple method. The total work is then O(N log N) where N is the dimensions of the covariance matrix in contrast to the usual O(N2) matrix-vector multiplication complexity. Error bounds exist for the matrix factorizations. We provide some simple computations to illustrate the ideas developed in the paper.
A study is made of a non-smooth optimization problem arising in adaptive-optics, which involves the real-time control of a deformable mirror designed to compensate for atmospheric turbulence and other dynamic image degradation factors. One formulation of this problem yields a functional f(U) equals (Sigma) iequals1n maxj[(UTMjU)ii] to be maximized over orthogonal matrices U for a fixed collection of n X n symmetric matrices Mj. We consider first the situation which can arise in practical applications where the matrices Mj are nearly pairwise commutative. Besides giving useful bounds, results for this case lead to a simple corollary providing a theoretical closed-form solution for globally maximizing f if the Mj are simultaneously diagonalizable. However, even here conventional optimization methods for maximizing f are not practical in a real-time environment. The genal optimization problem is quite difficult and is approached using a heuristic Jacobi-like algorithm. Numerical test indicate that the algorithm provides an effective means to optimize performance for some important adaptive-optics systems.
The performance of a closed loop adaptive optics system may in principle be improved by selecting distinct and independently optimized control bandwidths for separate components, or modes, of the wave front distortion profile. In this paper we outline a method for synthesizing and optimizing a multi-bandwidth adaptive optics control system from performance estimates previously derived for single-bandwidth control systems operating over a range of bandwidths. Numerical results are presented for use of an atmospheric turbulence profile consisting of a single translating phase screen with Kolmogorov statistics, a Shack-Hartmann wave front sensor with 8 subapertures across the aperture of the telescope, and a continuous facesheet deformable mirror with actuators conjugate with the corners of the wave front sensor subapertures. The use of multiple control bandwidths significantly relaxes the wave front sensor noise level allowed for the adaptive optics system to operate near the performance limit imposed by fitting error. Nearly all of this reduction is already achieved through the use of a control system utilizing only two distinct bandwidths, one of which is the zero bandwidth.
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