W. L. Anderson, Ph.D., Professor, Electrical and Computer Engineering, UH
In previous work we have shown how to employ Fourier optical processing methods for two-dimensional wavelet transformation. The principles are: (l) 2D correlation using a suitably designed filter in the back focal plane of a Fourier transforming lens and (2) scaling, implemented (in one realization) by inter-element distance adjustment in the optical system. This project is an investigation of the mathematical properties of certain especially promising types of the optically-scaled correlations, methods of obtaining them experimentally, and areas of application.
The utility of these for 2D data reduction is strikingly illustrated for an holographic particle velocimetry (HPV) project in collaboration with Prof. F. Hussain, Mechanical Engineering Department. The purpose is the study of turbulent fluid flow seeded with small particles. A double-exposure holographic "snapshot" gives a sampling of vector fluid flow in the illuminated volume. Digital processing of the hologram requires treatment of order 1011 bits of information for a 2x2 cm area of hologram; moreover, major amounts of operator intervention are required while the procedure is under way. The useful information, that of particle locations, consists of only about 35 bits. It is evident that converting from analog to digital format before beginning data reduction is ludicrously inefficient.
With a hybrid coherent optics digital system the entire area of any depth plane within the system of particles can be processed in parallel, literally at the speed of light. Although depth search requires time for a mechanical traverse to effect the scaling, even modest CCD camera framing rates could read out all the data to a workstation automatically in a matter of minutes, rather than the days or even weeks now considered standard for a single hologram. In the future, mechanically mediated depth search could be circumvented using a digitally addressed spatial light modulator (SLM) in the transform plane to perform the scaling by digital command. Cinematographic HPV enabling 4D space-time sampling of vector velocity flow, a goal fervently desired by researchers, will remain unattainable unless optical processing is put to use in its behalf.
Figure l. Numerically simulated comparison of correlation peak for matched filtering (left) with that for a POF filter (right) using only the phase part of the matched filter spectrum (see Fig. 2).
When the filter used to obtain the correlation is the conjugate of the Fourier transform of the object to be detected, it is called a matched filter, and the output is the autocorrelation. In the class of linear filters, the matched filter is optimum with respect to maximizing signal/noise ratio at a point. Methods of nonlinear filtering can, however, give substantial improvement, as seen in Fig. 1 for one choice of a phase-only-filter (POF). Because optimality can not be shown, study must rely on laboratory experimentation and numerical simulation. The former is not an option for us now, but requests for the transform lenses needed are contained (or intrinsic) in proposals and preproposals that have been submitted. Numerical simulation is lengthy, since a Mie scattering program is used for each plot.
Figure 2. The phase portion (only) of the diffraction under conditions as in Fig. l.
Surprisingly, phase patterns for diffraction, Fig. 2, are much simpler than magnitude patterns, Fig. 3, and will be easier to synthesize. The POF is considerably superior to the matched filter performance which, in turn, is orders of magnitude superior to incoherent detection, the current method of choice.
Figure 3. The relative intensity (magnitude squared) of diffraction under conditions as in Figs. l and 2.
Criteria of superiority here include (l) immunity to noise, (2) resolution (lateral and depth), and (3) sensitivity (magnitude of response, i.e., correlation peak magnitude). These characteristics, together with the others intrinsic to optical correlation, make this type of processing eminently suitable to automation, hence to extremely rapid and efficient data compression.
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Farokh B. Bastani, Ph.D., Professor, Computer Science, UH
Accurate assessment of software reliability is necessary for safety-critical systems such as space vehicles. This goal has proven elusive in spite of efforts comprising more than two decades of research. We are investigating a novel approach that combines program transformation with statistical testing. During 1994-1995, our work focused on developing the theoretical foundation as well as a set of tools to automate the approach.
The types of transformations under consideration are those which amplify the effect of test cases, i.e., simple transformations that allow us to infer the behavior of the program for many inputs based on its behavior for one input. Thus, these transformation rules reduce the effective size of the input space, typically by eliminating one or more dimensions in the input space. The major benefit of these transformations is to make the reliability estimate insensitive to the operational profile. Also, when the transformed input space is sufficiently small, sampling without replacement can be used to significantly reduce the number of test cases needed for achieving a desired confidence level.
Bojan Cukic is investigating these techniques as part of his doctoral dissertation. We have developed several transformation rules, including program slicing, elimination of nondeterministic control structures, and input, and output transformations for amplifying test cases. We are also developing monotonic transformation rules that significantly accelerate the execution of each test case. The key idea for achieving performance speed-up is to ensure that the correctness of the transformed program for an input implies correctness of the original program for that input. However, unlike semantically equivalent transformations, if the transformed version is incorrect then the original version must be tested to determine its behavior for that particular input.
Three major software tools are being developed to automate the evaluation process, specifically, a symbolic execution system, an automated test data generation system, and an input space visualization system.
Ridhdhish Amin, a master's student, is implementing a symbolic execution system for C programs using SAGE++ as the underlying parser. This tool generates the path constraints and output expressions in algebraic form for use by the test data generator and visualization system. A first version is ready and is being applied to an avionics program for controlling the landing phase of an aircraft.
As part of his doctoral dissertation, Anouar Jamoussi is developing an accelerated test data generator based on a two-step approach to achieve a speedup of over 200 times over conventional interpretive methods of generating random test data that satisfy a given partition predicate. In the first step, heuristics are used to order the input parameters needed to obtain an optimal sequence for generating the test data. Next, a customized test data generator is automatically coded for each predicate, compile, and linked to the application program. A prototype is ready, and work is in progress to statistically bound each predicate by a tight box to increase the "hit ratio" in the random test data generation process.
Victoria Hilford, a doctoral student, is developing a program for visualizing the input space of process-control programs. The program uses the predicates and expressions from the symbolic execution system, as well as data from the testing phase, to construct and display a multidimensional profile of the tested portions of the input space. Its main use will be to identify areas in the input space that need additional testing. Ms. Hilford is porting an earlier prototype for NeXt machines to the SUN-Unix environment.
To validate the approach and the tools, we have obtained the specification of an avionics program from Dr. Michael Lyu at AT&T Bell Labs. The program, developed by Somdutt Behura as part of a special problems course, was rigorously reviewed by all members of the research group, including Nidal Zeidat, a doctoral student. The program has been sent to Dr. Lyu for acceptance testing and will then undergo detailed evaluation by our group.
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ISSO -- Institute for Space Systems Operations
1994-1995 Annual Report
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