# Optimization

## Group leader: Hongjian Wang

## Projects:

__DFG project: Ultrasound Computed Tomography__

Researcher: Hongjian Wang

In cooperation with the Karlsruhe Institute of Technology (KIT) we are developing a new class of reconstruction techniques for three-dimensional Ultrasound Computed Tomography (3D-USCT). The main challenge of USCT is twofold: a forward model achieving a high-enough accuracy (here, by using a paraxial approximation); a sufficiently fast reconstruction which is a local optimization of parameter estimation problem. Our part is focused on the second point, where new optimization strategies and variants that have found widespread use in standard tomography problems will be further developed. The methods have to be re-investigated in the context of ultrasound transmission tomography since we now deal with a nonlinear model, and also adaptations of the optimization framework have to take place, e.g. the adaptation of preconditioned conjugate gradient, Tikhonov regularization, and multigrid method.

- Preconditioned Conjugate Gradient for USCT Image Reconstruction

USCT image reconstruction is an inverse problem which is solved iteratively based on a forward model of the Helmholtz equation by paraxial approximation and thus is time-consuming. We solve the inverse problem in a two-level strategy by an outer and an inner loop. At each iteration of the outer loop, the system is linearized and this linear subproblem is solved in the inner loop with a preconditioned conjugate gradient (CG). A standard Cholesky preconditioning method based on the system matrix is compared with a matrix-free Quasi-Newton update approach, where a preconditioned matrix-vector product is computed at the beginning of every CG iteration [1].

__ZIM project: Intensity-modulated skin irradiation__

Researcher: Alexander Stadler

The aim of the project is to develop an intensity-modulated surface irradiation system based on the ioRT-50 source from Wolf Medizintechnik GmbH for the treatment of skin tumors.

__ZIM project: Optimal ablation planning for a laser-based vision correction__

Researcher: Leoni Neubauer

### The aim of the project is to implement an optimal refractive surgical intervention, which has a minimum of roughness in the ablation of the cornea. In this process, tissues of the cornea are removed with many laser pulses until the optical properties of the cornea correspond to the desired target. The ablated volume of a single laser pulse is much smaller than the total removal volume. For this reason, several laser pulses are sequentially delivered to the cornea. Each laser pulse locally ablates a small amount of corneal tissue. Overall, a global erosion is achieved. This project leads to a new class of therapies in ophthalmology based on new technologies.

### References

- Wang H, Gemmeke H, Hopp T, Hesser J. USCT Image Reconstruction: Acceleration using Gauss-Newton Preconditioned Conjugate Gradient. In: International Workshop on Medical Ultrasound Tomography. International Workshop on Medical Ultrasound Tomography. Speyer, Germany; 2017.