International Workshop on Medical Ultrasound Tomography

USCT Image Reconstruction: Acceleration using Gauss-Newton Preconditioned Conjugate Gradient

Nov 1, 2017, 11:00 AM

20m

Lecture Hall

Oral Main Track Session 2: Imaging and inversion II

Speaker

Hongjian Wang (Heidelberg University)

Description

Ultrasound transmission tomography offers quantitative characterization of the tissue or materials by their speed of sound and attenuation. Reconstruction of such images is an inverse problem which is solved iteratively based on a forward model of paraxial approximation of the Helmholtz equation and thus is time-consuming. Hence, developing optimizers that decrease this time, in particular reducing the number of forward propagations is important for clinical practice.

(3) Results

The Cholesky preconditioning reduces the CG iteration by approx. 70%~85%; yet the computation time for determining the system matrix as the input for the matrix factorization function is dominating, offsetting the gains of the reduction of iterations. The matrix-free preconditioning method saves approx. 30% of the computation time on average for single-frequency reconstruction and the multi-frequency reconstruction. For the stable multi-frequency reconstruction, we test three breast-like numerical phantoms resulting in a deviation of 0.13 m/s on average in speed of sound reconstruction and a deviation of 5.4% on average in attenuation reconstruction from the ground truth.

(2) Material and Methods

We solve the inverse problem of reconstruction 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 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. We also use a multigrid scheme with a multi-frequency reconstruction to firstly get a convergent rough reconstruction at a lower frequency and then refine it on a higher-resolution grid as the starting solution of higher frequency reconstruction.

(4) Discussion and Conclusion

Compared with the Cholesky preconditioning, the matrix-free preconditioner via Quasi-Newton updating can actually save computation time. More effective problem-dependent spatial preconditioning techniques will be studied for our USCT image reconstruction. Especially for the multigrid reconstruction framework, the non-uniform convergence rates for coarse scale features and fine scale features should be taken into consideration.