Publications

Displaying 1 - 25 of 33

Data assimilation in 2D nonlinear advection diffusion equations, using an explicit stabilized leapfrog scheme run backward in time.

July 12, 2022

Author(s)

Alfred S. Carasso

With an artificial example of a 2D nonlinear advection diffusion equation on the unit square this paper considers the data assimilation problem of finding initial values that can evolve into a close approximation to a desired target result at some

Data assimilation in 2D Burgers equation using a stabilized explicit scheme run backward in time

December 9, 2021

Author(s)

Alfred S. Carasso

STABILIZED LEAPFROG SCHEME RUN BACKWARD IN TIME,AND THE EXPLICIT O(?t)^2 STEPWISE COMPUTATION OFILL-POSED TIME-REVERSED 2D NAVIER-STOKES EQUATIONS

September 11, 2021

Author(s)

Alfred S. Carasso

Richardson's leapfrog scheme is notoriously unconditionally unstable in well-posed, forward, linear dissipative evolution equations. Remarkably, that scheme can be stabilized, marched backward in time, and provide useful reconstructions in an interesting

COMPUTING ILL-POSED TIME-REVERSED 2D NAVIER-STOKES EQUATIONS, USING A STABILIZED EXPLICIT DIFFERENCE SCHEME MARCHING BACKWARD IN TIME

December 6, 2019

Author(s)

Alfred S. Carasso

Abstract. This paper constructs an unconditionally stable explicit difference scheme, marching backward in time, that can solve an interesting, but limited class of ill-posed, time-reversed 2D incompressible Navier-Stokes initial value problems. Stability

Stable explicit stepwise marching scheme in ill-posed time-reversed 2D Burgers' Equation

September 1, 2018

Author(s)

Alfred S. Carasso

This paper constructs an unconditionally stable explicit difference scheme, marching backward in time, that can solve an important, but limited, class of time-reversed 2D Burgers' initial value problems. Stability is achieved by applying a compensating

Stabilized backward in time explicit marching schemes in the numerical computation of ill-posed time-reversed hyperbolic/parabolic systems

March 7, 2018

Author(s)

Alfred S. Carasso

This paper develops stabilized explicit marching difference schemes that can successfully solve a significant but {\em limited} class of multidimensional, ill-posed, backward in time problems for coupled hyperbolic/parabolic systems associated with

Stable explicit stepwise marching scheme in ill-posed time-reversed viscous wave equations

August 12, 2015

Author(s)

Alfred S. Carasso

The numerical computation of ill-posed, nonlinear, multidimensional initial value problems presents considerable difficulties. Conventional stepwise marching schemes for such problems, whether explicit or implicit, are necessarily unconditionally unstable

Stable explicit time marching in well-posed or ill-posed nonlinear parabolic equations.

July 27, 2015

Author(s)

Alfred S. Carasso

This paper analyzes an effective technique for stabilizing pure explicit time differencing in the numerical computation of multidimensional nonlinear parabolic equations. The method uses easily synthesized linear smoothing operators at each time step to

Compensating operators and stable backward in time marching in nonlinear parabolic equations.

March 1, 2014

Author(s)

Alfred S. Carasso

Step by step time-marching schemes are fundamental tools in the numerical exploration of well-posed nonlinear evolutionary partial differential equations. However, when the initial value problem is ill-posed, such stepwise time-marching numerical schemes

Compensating operators and stable backward in time marching in nonlinear parabolic equations.

November 26, 2013

Author(s)

Alfred S. Carasso

The use of `slow motion' L\'{e}vy stable fractional diffusion smoothing in alternative methods of latent fingerprint enhancement}

April 30, 2013

Author(s)

Alfred S. Carasso

Photoshop processing\footnote{Mention of commmercial products or services in this report does not imply NIST appproval or endorsement of these products or services, nor does it imply that such products or services are necessarily the best available for the

HAZARDOUS CONTINUATION BACKWARD IN TIME IN NONLINEAR PARABOLIC EQUATIONS AND AN EXPERIMENT IN DEBLURRING NONLINEARLY BLURRED IMAGERY

April 25, 2013

Author(s)

Alfred S. Carasso

Identifying sources of ground water pollution, and deblurring nanoscale imagery, as well as astronomical galaxy images, often involves the numerical computation of parabolic equations backward in time. However, very little computational experience has so

Alternative methods of latent fingerprint enhancement and metrics for comparing them

January 14, 2013

Author(s)

Alfred S. Carasso

Digital enhancements of latent fingerprints using Photoshop processing is the preferred methodology among law enforcement forensic experts. This report explores alternative enhancement methods that are independent of Photoshop, relying instead on such

Reconstructing the past from imprecise knowledge of the present: Some examples of non uniqueness in solving parabolic equations backward in time.

May 24, 2012

Author(s)

Alfred S. Carasso

Identifying sources of ground water pollution, and deblurring astronomical galaxy images, are two important applications generating growing interest in the numerical computation of parabolic equations backward in time. However, while backward uniqueness

Fractional Diffusion, Low Exponent Levy Stable Laws, and Slow Motion Denoising of Helium Ion Microscope Nanoscale Imagery

February 22, 2012

Author(s)

Andras Vladar, Alfred S. Carasso

Helium ion microscopes (HIM) are capable of acquiring images with better than 1nm resolution, and HIM images are particularly rich in morphological surface details. However, such images are generally quite noisy. A major challenge is to denoise these

Reconstructing the Past From Imprecise Knowledge of the Present: Some Examples of Non Uniqueness in Solving Parabolic Equations Backward in Time

April 13, 2011

Author(s)

Alfred S. Carasso

Bochner Subordination, Logarithmic Diffusion Equations, and Blind Deconvolution of Hubble Space Telescope Imagery and Other Scientific Data

November 30, 2010

Author(s)

Alfred S. Carasso

Generalized Linnik processes and associated logarithmic diffusion equations can be constructed by appropriate Bochner randomization of the time variable in Brownian motion and the related heat conduction equation. Remarkably, generalized Linnik

FRACTIONAL DIFFUSION, LOW EXPONENT LEVY STABLE LAWS, AND SLOW MOTION DENOISING OF HELIUM ION MICROSCOPE NANOSCALE IMAGERY

September 30, 2010

Author(s)

Alfred S. Carasso, Andras Vladar

Bochner Subordination, Logarithmic Diffusion Equations, and Blind Deconvolution of Hubble Space Telescope Imagery and Other Scientific Data

September 23, 2009

Author(s)

Alfred S. Carasso

False Characteristic Functions and Other Pathologies in Variational Blind Deconvolution. A Method of Recovery.

September 9, 2009

Author(s)

Alfred S. Carasso

Given a blurred image g(x, y), variational blind deconvolution seeks to reconstruct both the unknown blur k(x, y), and the unknown sharp image f(x, y), by minimizing an appropriate cost functional. This paper restricts attention to a rich and significant

Calibrating Image Roughness by Estimating Lipschitz Exponents, with Applications to Image Restoration

March 3, 2008

Author(s)

Alfred S. Carasso

Most commonly occurring images f(x,y) are not smoothly differentiable functions of the variables x and y. Rather, these images display edges, localized sharp features, and other significant fine scale details or texture. Correct characterization and

Calibrating Image Roughness by Estimating Lipschitz Exponents, with Applications to Image Restoration

August 1, 2007

Author(s)

Alfred S. Carasso, Andras Vladar

APEX Blind Deconvolution of Color Hubble Space Telescope Imagery and Other Astronomical Data

October 1, 2006

Author(s)

Alfred S. Carasso

The APEX method is a non-iterative, single frame, direct blind deconvolution technique that can sharpen certain kinds of high resolution images in quasi real-time. The method is predicated on a restricted class of blurs, in the form of 2D heavy-tailed bell

APEX Blind Deconvolution of Real Hubble Space Telescope Imagery and Other Astronomical Data

October 1, 2006

Author(s)

Alfred S. Carasso

APEX Blind Deconvolution of Real Hubble Space Telescope Imagery and Other Astronomical Data

December 2, 2005

Author(s)

Alfred S. Carasso

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