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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

An adaptive technique to maximize lossless image data compression of satellite images

Data compression will pay an increasingly important role in the storage and transmission of image data within NASA science programs as the Earth Observing System comes into operation. It is important that the science data be preserved at the fidelity the instrument and the satellite communication systems were designed to produce. Lossless compression must therefore be applied, at least, to archive the processed instrument data. In this paper, we present an analysis of the performance of lossless compression techniques and develop an adaptive approach which applied image remapping, feature-based image segmentation to determine regions of similar entropy and high-order arithmetic coding to obtain significant improvements over the use of conventional compression techniques alone. Image remapping is used to transform the original image into a lower entropy state. Several techniques were tested on satellite images including differential pulse code modulation, bi-linear interpolation, and block-based linear predictive coding. The results of these experiments are discussed and trade-offs between computation requirements and entropy reductions are used to identify the optimum approach for a variety of satellite images. Further entropy reduction can be achieved by segmenting the image based on local entropy properties then applying a coding technique which maximizes compression for the region. Experimental results are presented showing the effect of different coding techniques for regions of different entropy. A rule-base is developed through which the technique giving the best compression is selected. The paper concludes that maximum compression can be achieved cost effectively and at acceptable performance rates with a combination of techniques which are selected based on image contextual information.

Stewart, Robert J.↗
NASA NTRS1994

A Planar Approximation for the Least Reliable Bit Log-likelihood Ratio of 8-PSK Modulation

The optimum decoding of component codes in block coded modulation (BCM) schemes requires the use of the log-likelihood ratio (LLR) as the signal metric. An approximation to the LLR for the least reliable bit (LRB) in an 8-PSK modulation based on planar equations with fixed point arithmetic is developed that is both accurate and easily realizable for practical BCM schemes. Through an error power analysis and an example simulation it is shown that the approximation results in 0.06 dB in degradation over the exact expression at an E(sub s)/N(sub o) of 10 dB. It is also shown that the approximation can be realized in combinatorial logic using roughly 7300 transistors. This compares favorably to a look up table approach in typical systems.

Thesling, William H.↗
NASA NTRS1994

Lossless compression of NOAA-AVHRR satellite data

A high-performance lossless compression system for satellite NOAA data is developed. The data is called 'high resolution picture transmission' (HRPT) data, and consists of around 93 percent advanced very high resolution radiometer (AVHRR) multi-channel image data and 7 percent of miscellaneous data. In compressing the image portion, we classify each pixel into 10 different groups and apply a multi-channel prediction and a non-linear error conversion. The entropy coder is an arithmetic coder which is adaptive and regenerates the approximation of the statistical properties of the source as an initial probability table. To compress the non-image part, we used the general compressor (gzip). From experimental results, the original information is compressed down to 25 percent to approx. 40 percent.

Takamura, Seishi↗
NASA NTRS1994

Open architectures for formal reasoning and deductive technologies for software development

The objective of this project is to develop an open architecture for formal reasoning systems. One goal is to provide a framework with a clear semantic basis for specification and instantiation of generic components; construction of complex systems by interconnecting components; and for making incremental improvements and tailoring to specific applications. Another goal is to develop methods for specifying component interfaces and interactions to facilitate use of existing and newly built systems as 'off the shelf' components, thus helping bridge the gap between producers and consumers of reasoning systems. In this report we summarize results in several areas: our data base of reasoning systems; a theory of binding structures; a theory of components of open systems; a framework for specifying components of open reasoning system; and an analysis of the integration of rewriting and linear arithmetic modules in Boyer-Moore using the above framework.

Mccarthy, John↗
NASA NTRS1994

A simplified Integer Cosine Transform and its application in image compression

A simplified version of the integer cosine transform (ICT) is described. For practical reasons, the transform is considered jointly with the quantization of its coefficients. It differs from conventional ICT algorithms in that the combined factors for normalization and quantization are approximated by powers of two. In conventional algorithms, the normalization/quantization stage typically requires as many integer divisions as the number of transform coefficients. By restricting the factors to powers of two, these divisions can be performed by variable shifts in the binary representation of the coefficients, with speed and cost advantages to the hardware implementation of the algorithm. The error introduced by the factor approximations is compensated for in the inverse ICT operation, executed with floating point precision. The simplified ICT algorithm has potential applications in image-compression systems with disparate cost and speed requirements in the encoder and decoder ends. For example, in deep space image telemetry, the image processors on board the spacecraft could take advantage of the simplified, faster encoding operation, which would be adjusted on the ground, with high-precision arithmetic. A dual application is found in compressed video broadcasting. Here, a fast, high-performance processor at the transmitter would precompensate for the factor approximations in the inverse ICT operation, to be performed in real time, at a large number of low-cost receivers.

Costa, M.↗
NASA NTRS1994

Low-complexity wavelet filter design for image compression

Image compression algorithms based on the wavelet transform are an increasingly attractive and flexible alternative to other algorithms based on block orthogonal transforms. While the design of orthogonal wavelet filters has been studied in significant depth, the design of nonorthogonal wavelet filters, such as linear-phase (LP) filters, has not yet reached that point. Of particular interest are wavelet transforms with low complexity at the encoder. In this article, we present known and new parameterizations of the two families of LP perfect reconstruction (PR) filters. The first family is that of all PR LP filters with finite impulse response (FIR), with equal complexity at the encoder and decoder. The second family is one of LP PR filters, which are FIR at the encoder and infinite impulse response (IIR) at the decoder, i.e., with controllable encoder complexity. These parameterizations are used to optimize the subband/wavelet transform coding gain, as defined for nonorthogonal wavelet transforms. Optimal LP wavelet filters are given for low levels of encoder complexity, as well as their corresponding integer approximations, to allow for applications limited to using integer arithmetic. These optimal LP filters yield larger coding gains than orthogonal filters with an equivalent complexity. The parameterizations described in this article can be used for the optimization of any other appropriate objective function.

Majani, E.↗
NASA NTRS1992

An implementation of the QMR method based on coupled two-term recurrences

The authors have proposed a new Krylov subspace iteration, the quasi-minimal residual algorithm (QMR), for solving non-Hermitian linear systems. In the original implementation of the QMR method, the Lanczos process with look-ahead is used to generate basis vectors for the underlying Krylov subspaces. In the Lanczos algorithm, these basis vectors are computed by means of three-term recurrences. It has been observed that, in finite precision arithmetic, vector iterations based on three-term recursions are usually less robust than mathematically equivalent coupled two-term vector recurrences. This paper presents a look-ahead algorithm that constructs the Lanczos basis vectors by means of coupled two-term recursions. Implementation details are given, and the look-ahead strategy is described. A new implementation of the QMR method, based on this coupled two-term algorithm, is described. A simplified version of the QMR algorithm without look-ahead is also presented, and the special case of QMR for complex symmetric linear systems is considered. Results of numerical experiments comparing the original and the new implementations of the QMR method are reported.

Freund, Roland W.↗
NASA NTRS1995

Kepler Equation solver

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.

Markley, F. Landis↗
NASA NTRS1994

Precision waveform shaping and precompensation for high data rate space coomunications systems

This paper studies a memory-based pulse shaping and traveling wave tube precompensation technique applied to high data rate satellite communications. Baseband I and Q waveforms are synthesized from data stored in a distributed arithmetic architecture. The waveforms are adjusted to minimize intersymbol interference spectral bandwidth and traveling wave tube distortion. We evaluate its performance in a simulated bi-phase shift keying (BPSK) link. The results show that memory-based precompensation has great potential to improve link performance.

Tague, John A.↗
NASA NTRS1994

Kupier prize lecture: Sources of solar-system carbon

We have tried to deconvolve Solar-System carbon into its sources, on the basis of C-12/C-13 ratios (equivalent to R). Interstellar SiC in meteorites, representing greater than 4.6-Ga-old stardust from carbon stars, is isotopically heavier (bar R = 38 +/- 2) than Solar-System carbon (89), implying that the latter contains an additional, light component. A likely source are massive stars, mainly Type II supernovae and Wolf-Rayet stars, which, being O-rich, eject their C largely as CO rather than carbonaceous dust. The fraction of such light C in the Solar System depends on R(sub light) in the source. For R(sub light) = 180-1025 (as in 'Group 4' meteoritic graphite spherules, which apparently came from massive stars greater than 4.6 Ga ago), the fraction of light C is 0.79-0.61. Similar results are obtained for present-day data on red giants and interstellar gas. Although both have become enriched in C-13 due to galactic evolution (to bar-R = 20 and 57), the fraction of the light component in interstellar gas again is near 0.7. (Here bar R represents the mean of a mixture calculated via atom fractions; it is not identical to the arithmetic mean R). Interstellar graphite, unlike SiC, shows a large peak at R approximately equal 90, near the solar value. Although some of the grains may be of local origin, others show anomalies in other elements and hence are exotic. Microdiamonds, with R = 93, also are exotic on the basis of their Xe and N. Apparently R approximately 90 was a fairly common composition 4.6 Ga ago, of stars as well as the ISM.

Anders, Edward↗
NASA NTRS1995

Interactive Software For Astrodynamical Calculations

QUICK computer program provides user with facilities of sophisticated desk calculator performing scalar, vector, and matrix arithmetic; propagate conic-section orbits; determines planetary and satellite coordinates; and performs other related astrodynamic calculations within FORTRAN-like software environment. QUICK is interpreter, and no need to use compiler or linker to run QUICK code. Outputs plotted in variety of formats on variety of terminals. Written in RATFOR.

Schlaifer, Ronald S.↗
NASA NTRS1995

Reducing Truncation Error In Integer Processing

Improved method of rounding off (truncation of least-significant bits) in integer processing of data devised. Provides for reduction, to extremely low value, of numerical bias otherwise generated by accumulation of truncation errors from many arithmetic operations. Devised for use in integer signal processing, in which rescaling and truncation usually performed to reduce number of bits, which typically builds up in sequence of operations. Essence of method to alternate direction of roundoff (plus, then minus) on alternate occurrences of truncated values contributing to bias.

Thomas, J. Brooks↗
NASA NTRS1995

Formal development of a clock synchronization circuit

This talk presents the latest stage in formal development of a fault-tolerant clock synchronization circuit. The development spans from a high level specification of the required properties to a circuit realizing the core function of the system. An abstract description of an algorithm has been verified to satisfy the high-level properties using the mechanical verification system EHDM. This abstract description is recast as a behavioral specification input to the Digital Design Derivation system (DDD) developed at Indiana University. DDD provides a formal design algebra for developing correct digital hardware. Using DDD as the principle design environment, a core circuit implementing the clock synchronization algorithm was developed. The design process consisted of standard DDD transformations augmented with an ad hoc refinement justified using the Prototype Verification System (PVS) from SRI International. Subsequent to the above development, Wilfredo Torres-Pomales discovered an area-efficient realization of the same function. Establishing correctness of this optimization requires reasoning in arithmetic, so a general verification is outside the domain of both DDD transformations and model-checking techniques. DDD represents digital hardware by systems of mutually recursive stream equations. A collection of PVS theories was developed to aid in reasoning about DDD-style streams. These theories include a combinator for defining streams that satisfy stream equations, and a means for proving stream equivalence by exhibiting a stream bisimulation. DDD was used to isolate the sub-system involved in Torres-Pomales' optimization. The equivalence between the original design and the optimized verified was verified in PVS by exhibiting a suitable bisimulation. The verification depended upon type constraints on the input streams and made extensive use of the PVS type system. The dependent types in PVS provided a useful mechanism for defining an appropriate bisimulation.

Miner, Paul S.↗
NASA NTRS1995

Interpretation of IEEE-854 floating-point standard and definition in the HOL system

The ANSI/IEEE Standard 854-1987 for floating-point arithmetic is interpreted by converting the lexical descriptions in the standard into mathematical conditional descriptions organized in tables. The standard is represented in higher-order logic within the framework of the HOL (Higher Order Logic) system. The paper is divided in two parts with the first part the interpretation and the second part the description in HOL.

MULTIPLICATION SUBTRACTION↗
NASA NTRS1994

A Feasibility Study for Perioperative Ventricular Tachycardia Prognosis and Detection and Noise Detection Using a Neural Network and Predictive Linear Operators

To locate the accessory pathway(s) in preexicitation syndromes, epicardial and endocardial ventricular mapping is performed during anterograde ventricular activation via accessory pathway(s) from data originally received in signal form. As the number of channels increases, it is pertinent that more automated detection of coherent/incoherent signals is achieved as well as the prediction and prognosis of ventricular tachywardia (VT). Today's computers and computer program algorithms are not good in simple perceptual tasks such as recognizing a pattern or identifying a sound. This discrepancy, among other things, has been a major motivating factor in developing brain-based, massively parallel computing architectures. Neural net paradigms have proven to be effective at pattern recognition tasks. In signal processing, the picking of coherent/incoherent signals represents a pattern recognition task for computer systems. The picking of signals representing the onset ot VT also represents such a computer task. We attacked this problem by defining four signal attributes for each potential first maximal arrival peak and one signal attribute over the entire signal as input to a back propagation neural network. One attribute was the predicted amplitude value after the maximum amplitude over a data window. Then, by using a set of known (user selected) coherent/incoherent signals, and signals representing the onset of VT, we trained the back propagation network to recognize coherent/incoherent signals, and signals indicating the onset of VT. Since our output scheme involves a true or false decision, and since the output unit computes values between 0 and 1, we used a Fuzzy Arithmetic approach to classify data as coherent/incoherent signals. Furthermore, a Mean-Square Error Analysis was used to determine system stability. The neural net based picking coherent/incoherent signal system achieved high accuracy on picking coherent/incoherent signals on different patients. The system also achieved a high accuracy of picking signals which represent the onset of VT, that is, VT immediately followed these signals. A special binary representation of the input and output data allowed the neural network to train very rapidly as compared to another standard decimal or normalized representations of the data.

Moebes, T. A.↗
NASA NTRS1996

Progressive transmission and compression images

We describe an image data compression strategy featuring progressive transmission. The method exploits subband coding and arithmetic coding for compression. We analyze the Laplacian probability density, which closely approximates the statistics of individual subbands, to determine a strategy for ordering the compressed subband data in a way that improves rate-distortion performance. Results are presented for a test image.

Kiely, A. B.↗
NASA NTRS1996

Preconditioning Operators on Unstructured Grids

We consider systems of mesh equations that approximate elliptic boundary value problems on arbitrary (unstructured) quasi-uniform triangulations and propose a method for constructing optimal preconditioning operators. The method is based upon two approaches: (1) the fictitious space method, i.e., the reduction of the original problem to a problem in an auxiliary (fictitious) space, and (2) the multilevel decomposition method, i.e., the construction of preconditioners by decomposing functions on hierarchical meshes. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh step. The preconditioner has an optimal computational cost: the number of arithmetic operations required for its implementation is proportional to the number of unknowns in the problem. The construction of the preconditioning operators for three dimensional problems can be done in the same way.

Nepomnyaschikh, S. V.↗
NASA NTRS1996

On the Rapid Computation of Various Polylogarithmic Constants

We give algorithms for the computation of the d-th digit of certain transcendental numbers in various bases. These algorithms can be easily implemented (multiple precision arithmetic is not needed), require virtually no memory, and feature run times that scale nearly linearly with the order of the digit desired. They make it feasible to compute, for example, the billionth binary digit of log(2) or pi on a modest workstation in a few hours run time. We demonstrate this technique by computing the ten billionth hexadecimal digit of pi, the billionth hexadecimal digits of pi-squared, log(2) and log-squared(2), and the ten billionth decimal digit of log(9/10). These calculations rest on the observation that very special types of identities exist for certain numbers like pi, pi-squared, log(2) and log-squared(2). These are essentially polylogarithmic ladders in an integer base. A number of these identities that we derive in this work appear to be new, for example a critical identity for pi.

Bailey, David H.↗