# 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… )

# Total Generalized Variation regularization for X-ray tomography – Experimental Data

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 Total ( continue reading… )

# Total variation regularization for X-ray tomography – Experimental Data

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 Total Variation ( 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… )

# The D-bar Method for Electrical Impedance Tomography – Simulated Data

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

# Total variation regularization for 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 Total ( 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… )

# Welcome to FIPS Computational Inversion Blog!

Author of this post: Samuli Siltanen (samuli.siltanen “at” helsinki.fi) This blog aims to help everyone interested in inverse problems and their computational solution. We offer open software and links to open datasets so that anyone can easily try different reconstruction methods on both simulated and measured data. Inverse problems are ( continue reading… )