RECONSTRUCTION AND ENHANCEMENT OF SIGNALS USING NON-OSCILLATORY SHOCK/TURBULENCE CAPTURING ALGORITHMS

THE CONCEPTS AND TECHNIQUES DEVELOPED IN THE NUMERICAL SOLUTION OF HYPERBOLIC CONSERVATION LAWS E.G. IN COMPRESSIBLE GAS DYNAMICS HAVE RECENTLY BEEN FOUND BY THIS COMPANY TO BE EXTREMELY RELEVANT TO THE PROBLEM OF RECONSTRUCTION AND ENHANCEMENT OF SIGNALS (INCLUDING IMAGES AND ACOUSTIC SIGNALS). BOTH SUBJECTS DEAL WITH THE DISCRETE REPRESENTATION OF DISCONTINUOUS FUNCTIONS. THE RELEVANT CONCEPTS INCLUDE VARIATION DIMINISHING OR ESSENTIALLY NON-OSCILLATORY (ENO) APPROXIMATIONS, THE NEED FOR NONLINEAR APPROXIMATIONS TO LINEAR PROBLEMS, AND COMPRESSIVE METHODS. A BREAKTHROUGH METHOD FOR PROBLEMS INVOLVING SHOCK-TURBULENCE INTERACTION, WHERE BOTH DISCONTINUITIES AND DETAILED FINE STRUCTURES ARE FOUND, INVOLVES USING HIGH ORDER ENO SCHEMES (1). THESE TECHNIQUES SHALL BE SUITABLY MODIFIED AND APPLIED TO THE COMPUTER RECONSTRUCTION AND ENHANCEMENT OF SIGNALS. THESE METHODS ARE LOCAL, NONLINEAR, AND INVOLVE THE DISCRETIZATION OF NEW, NONLINEAR, TIME DEPENDENT, PARTIAL DIFFERENTIAL EQUATIONS. THEY ARE "RINGING" FREE -SUPPRESSING SPUROUS "GHOSTS" (OSCILLATIONS) AND ARE CAPABLE OF REMOVING LARGE NOISE TO SIGNAL TO RATIOS, BLURRING TO SIGNAL RATIOS, AND CAN RESOLVE MULTIPLE SCALES. THEY ARE ALSO PERFECTLY SUITED FOR PARALLEL COMPUTERS.