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A fast temperature water vapor and ozone atmospheric profile retrieval algorithm is developed for the high spectral resolution Infrared Atmospheric Sounding Interferometer (IASI) space-borne instrument. Compression and de-noising of IASI observations are performed using Principal Component Analysis. This preprocessing methodology also allows, for a fast pattern recognition in a climatological data set to obtain a first guess. Then, a neural network using first guess information is developed to retrieve simultaneously temperature, water vapor and ozone atmospheric profiles. The performance of the resulting fast and accurate inverse model is evaluated with a large diversified data set of radiosondes atmospheres including rare events.
For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.
In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.
In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.
Algorithm for Fast Two Dimensional Fourier Transform requiring logarithm additions and multiplication
A bus system that can change dynamically to suit computational needs is referred to as reconfigurable. We present a fast adaptive convex hull algorithm on a two-dimensional processor array with a reconfigurable bus system (2-D PARBS, for short). Specifically, we show that computing the convex hull of a planar set of n points taken O(log n/log m) time on a 2-D PARBS of size mn x n with 3 less than or equal to m less than or equal to n. Our result implies that the convex hull of n points in the plane can be computed in O(1) time in a 2-D PARBS of size n(exp 1.5) x n.
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
In this paper a new algorithm, designated as Fast Invariant Imbedding algorithm, for solution of Poisson equation on vector and massively parallel MIMD architectures is presented. This algorithm achieves the same optimal computational efficiency as other Fast Poisson solvers while offering a much better structure for vector and parallel implementation. Our implementation on the Intel Delta and Paragon shows that a speedup of over two orders of magnitude can be achieved even for moderate size problems.
In this paper massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. We have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although this represents an optimal computation, due the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. We develop a novel algorithm, designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. Due to these features, our algorithm is significantly more efficient than other Fast Poisson Solvers for implementation on massively parallel architectures.
DBSCAN is a well-known density-based clustering algorithm to discover arbitrary shape clusters. While conceptually simple in serial, the algorithm is challenging to efficiently parallelize on manycore GPU architectures. Common pitfalls, such as asynchronous range query calls, result in high thread execution divergence in many implementations. In this paper, we propose a new framework for GPU-accelerated DBSCAN, and describe two tree-based algorithms within that framework. Both algorithms fuse the search for neighbors with updating cluster information, but differ in their treatment of dense regions of the data. We show that the time taken to compute clusters is at most twice that of determination of the neighbors. We compare the proposed algorithms with existing CPU and GPU implementations, and demonstrate their competitiveness and performance using a fast traversal structure (bounding volume hierarchy) for low dimensional data. We also show that the memory usage can be reduced by processing object neighbors dynamically without storing them.
Efficient onboard data compression can reduce the data volume from hyperspectral imagers on NASA and DoD spacecraft in order to return as much imagery as possible through constrained downlink channels. Lossless compression is important for signature extraction, object recognition, and feature classification capabilities. To provide onboard data compression, a hardware implementation of a lossless hyperspectral compression algorithm was developed using a field programmable gate array (FPGA). The underlying algorithm is the Fast Lossless (FL) compression algorithm reported in Fast Lossless Compression of Multispectral- Image Data (NPO-42517), NASA Tech Briefs, Vol. 30, No. 8 (August 2006), p. 26 with the modification reported in Lossless, Multi-Spectral Data Comressor for Improved Compression for Pushbroom-Type Instruments (NPO-45473), NASA Tech Briefs, Vol. 32, No. 7 (July 2008) p. 63, which provides improved compression performance for data from pushbroom-type imagers. An FPGA implementation of the unmodified FL algorithm was previously developed and reported in Fast and Adaptive Lossless Onboard Hyperspectral Data Compression System (NPO-46867), NASA Tech Briefs, Vol. 36, No. 5 (May 2012) p. 42. The essence of the FL algorithm is adaptive linear predictive compression using the sign algorithm for filter adaption. The FL compressor achieves a combination of low complexity and compression effectiveness that exceeds that of stateof- the-art techniques currently in use. The modification changes the predictor structure to tolerate differences in sensitivity of different detector elements, as occurs in pushbroom-type imagers, which are suitable for spacecraft use. The FPGA implementation offers a low-cost, flexible solution compared to traditional ASIC (application specific integrated circuit) and can be integrated as an intellectual property (IP) for part of, e.g., a design that manages the instrument interface. The FPGA implementation was benchmarked on the Xilinx Virtex IV LX25 device, and ported to a Xilinx prototype board. The current implementation has a critical path of 29.5 ns, which dictated a clock speed of 33 MHz. The critical path delay is end-to-end measurement between the uncompressed input data and the output compression data stream. The implementation compresses one sample every clock cycle, which results in a speed of 33 Msample/s. The implementation has a rather low device use of the Xilinx Virtex IV LX25, making the total power consumption of the implementation about 1.27 W.
The reported investigation represents a continuation of a study conducted by Reed and Truong (1979), who proposed a hybrid algorithm for computing the discrete Fourier transform (DFT). The proposed technique employs a Winograd-type algorithm in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. The implementation of the technique involves a considerable number of additions. The new investigation shows an approach which can reduce the number of additions significantly. It is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm.
The NPLOT (NASTRAN Plot) is an interactive computer graphics program for plotting undeformed and deformed NASTRAN finite element models. Developed at NASA's Goddard Space Flight Center, the program provides flexible element selection and grid point, ASET and SPC degree of freedom labelling. It is easy to use and provides a combination menu and command driven user interface. NPLOT also provides very fast hidden line and haloed line algorithms. The hidden line algorithm in NPLOT proved to be both very accurate and several times faster than other existing hidden line algorithms. A fast spatial bucket sort and horizon edge computation are used to achieve this high level of performance. The hidden line and the haloed line algorithms are the primary features that make NPLOT different from other plotting programs.
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of an m × n matrix with m ≈ n provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The resulting factorization is composed of O(log n) sparse factors, each containing O(n) nonzero entries. The factorization can be attained using O(n 3/2 log n) computation and O(n log n) memory resources. Furthermore, the proposed algorithm can be implemented in parallel and can apply to matrices with strong or weak admissibility conditions arising from surface integral equation solvers as well as multi-frontal-based finite-difference, finite-element, or finite-volume solvers. A distributed-memory parallel implementation of the algorithm demonstrates excellent scaling behavior.
A fast 3-D object recognition algorithm that can be used as a quick-look subsystem to the vision system for the Special-Purpose Dexterous Manipulator (SPDM) is described. Global features that can be easily computed from range data are used to characterize the images of a viewer-centered model of an object. This algorithm will speed up the processing by eliminating the low level processing whenever possible. It may identify the object, reject a set of bad data in the early stage, or create a better environment for a more powerful algorithm to carry the work further.
PDP-9 assembly language program and algorithm for fast Fourier transform
A progress report on the forward model and CO retrieval algorithm is presented. For the forward model, the fast-transmittance algorithm is discussed including monochromatic calculations, determination of fast-transmittance parameters, and regression errors. Simulations, retrieval technique, and sensitivity of the CO retrieval algorithm are discussed.