Theory of compressive modeling and simulation

Harold Szu; Jae Cha; Richard L. Espinola; Keith Krapels

doi:10.1117/12.2032322

29 May 2013 Theory of compressive modeling and simulation

Harold Szu, Jae Cha, Richard L. Espinola, Keith Krapels

Proceedings Volume 8750, Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XI; 875011 (2013) https://doi.org/10.1117/12.2032322
Event: SPIE Defense, Security, and Sensing, 2013, Baltimore, Maryland, United States

Abstract

Modeling and Simulation (M&S) has been evolving along two general directions: (i) data-rich approach suffering the curse of dimensionality and (ii) equation-rich approach suffering computing power and turnaround time. We suggest a third approach. We call it (iii) compressive M&S (CM&S); because the basic Minimum Free-Helmholtz Energy (MFE) facilitating CM&S can reproduce and generalize Candes, Romberg, Tao & Donoho (CRT&D) Compressive Sensing (CS) paradigm as a linear Lagrange Constraint Neural network (LCNN) algorithm. CM&S based MFE can generalize LCNN to 2^nd order as Nonlinear augmented LCNN. For example, during the sunset, we can avoid a reddish bias of sunlight illumination due to a long-range Rayleigh scattering over the horizon. With CM&S we can take instead of day camera, a night vision camera. We decomposed long wave infrared (LWIR) band with filter into 2 vector components (8~10μm and 10~12μm) and used LCNN to find pixel by pixel the map of Emissive-Equivalent Planck Radiation Sources (EPRS). Then, we up-shifted consistently, according to de-mixed sources map, to the sub-micron RGB color image. Moreover, the night vision imaging can also be down-shifted at Passive Millimeter Wave (PMMW) imaging, suffering less blur owing to dusty smokes scattering and enjoying apparent smoothness of surface reflectivity of man-made objects under the Rayleigh resolution. One loses three orders of magnitudes in the spatial Rayleigh resolution; but gains two orders of magnitude in the reflectivity, and gains another two orders in the propagation without obscuring smog . Since CM&S can generate missing data and hard to get dynamic transients, CM&S can reduce unnecessary measurements and their associated cost and computing in the sense of super-saving CS: measuring one & getting one’s neighborhood free .

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Harold Szu, Jae Cha, Richard L. Espinola, and Keith Krapels "Theory of compressive modeling and simulation", Proc. SPIE 8750, Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XI, 875011 (29 May 2013); https://doi.org/10.1117/12.2032322

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KEYWORDS

Long wavelength infrared

Passive millimeter wave sensors

Reflectivity

Rayleigh scattering

Atmospheric modeling

Atmospheric propagation

Picosecond phenomena

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