An Iterative Method for the Reconstruction of Two-Dimensional Density Distributions

Two-dimensional quantitative photoacoustic image reconstruction of absorption distributions in scattering media by use of a simple iterative method.

Photoacoustic imaging is a noninvasive biomedical imaging modality for visualizing the internal structure and function of soft tissues. Conventionally, an image proportional to the absorbed optical energy is reconstructed from measurements of light-induced acoustic emissions. We describe a simple iterative algorithm to recover the distribution of optical absorption coefficients from the image o...

Iterative reconstruction method for three-dimensional optoacoustic imaging

Three-dimensional optoacoustic imaging uses detection of laser-generated thermoelastic waves with an ultrasound sensor array. Integrated acoustic signals (velocity potentials) are back projected into the source volume to give a map of absorbed laser energy. Since the number of array elements and the receiving solid angle are limited, radial back projection produces artifacts such as back projec...

An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

An Opertional Method for The Numerical Solution of Two Dimensional Linear Fredholm Integral Equations With an Error Estimation

ITERATIVE METHOD FOR SOLVING TWO-DIMENSIONAL NONLINEAR FUZZY INTEGRAL EQUATIONS USING FUZZY BIVARIATE BLOCK-PULSE FUNCTIONS WITH ERROR ESTIMATION

In this paper, we propose an iterative procedure based on two dimensionalfuzzy block-pulse functions for solving nonlinear fuzzy Fredholm integralequations of the second kind. The error estimation and numerical stabilityof the proposed method are given in terms of supplementary Lipschitz condition.Finally, illustrative examples are included in order to demonstrate the accuracyand convergence of...