Modified Level Set Method

Summary: Tomography means reconstructing the internal structure of a physical object using the X-ray images of the object taken from different directions. Mathematically, the problem is to recover a non-negative function f(x) from a collection of the line integrals of f. Here we show how to solve a dynamic tomography ( continue reading… )

Automatic regularization parameter selection: controlled wavelet domain sparsity

Summary: Choosing the regularization parameter is a hard problem, for which many approaches exist. Here we discuss the recently developed and fully automatic method, called controlled wavelet domain sparsity (CWDS) in the context of X-ray tomography. This approach involves sparsity promoting regularization with respect to an orthogonal wavelet basis. The ( continue reading… )

The D-bar Method for Electrical Impedance Tomography – Experimental Data

Summary: Electrical Impedance Tomography (EIT) aims to recover the internal electrical conductivity of a physical body from electrode measurements of voltages and currents at the boundary. EIT has applications in medical imaging, underground prospecting, and nondestructive testing. The image reconstruction problem of EIT is a nonlinear and severely ill-posed inverse ( continue reading… )

Simple simulation of X-ray tomography

Summary: Tomography means reconstructing the internal structure of a physical body using X-ray images of the body taken from different directions. Mathematically, the problem is to recover a non-negative function f(x) from a collection of line integrals of f. Here we show how to solve the tomography problem using truncated ( continue reading… )