We review recent work on the development of inversion formulas for the inverse problem in optical tomography. Applications to the construction of fast image reconstruction algorithms are described. Our results are illustrated with numerical simulations and experiments in model systems.

In this work, we extend the finite-difference contrast source inversion (FDCSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media a...

The statistical independence between the distributions of different chromophores in tissue has previously been used for linear unmixing with independent component analysis (ICA). In this study, we propose exploiting this statistical property in a nonlinear model-based inversion method. The aim is to reduce the sensitivity of the inversion scheme to errors in the modelling of the fluence, and he...

The main purpose of this paper is to further clarify the complexity of the inversion method by using Niche Genetic Algorithms (NGA) to inverse the petrophysical property parameters. The improved BISQ model, presented in our earlier work, is chosen for the forward model in NGA. In this paper, the relationship between the sample number of the given wave response data and the inversion results, su...

We compare IGA to traditional numerical inversion on a geological application. We show that ‘a priori’ information and expert knowledge can overcome lack of accurate data and help convergence towards a satisfactory solution.

We develop the theory behind the Expectation Maximization algorithm and an exact inversion formula for the attenuated Radon transform, two reconstruction methods used in SPECT. We also implement both methods and present a few numerical experiments.

Kirchhoff inversion theory tells us that reflection data provides information about the Fourier transform of the reflectivity function at each point in the illuminated subsurface. Thus, inversion formulas expressed as integrals in image point coordinates that closely characterize that Fourier domain are attractive for their relative simplicity. On the other hand, integrals over source/receiver ...