Optimized transducer configuration for ultrasound waveform tomography in breast cancer detection

Waveform inversion is a promising method for ultrasound computed tomography able to produce high-resolution images of human breast tissue. However, the computational complexity of waveform inversion remains a considerable challenge, and the costs per iteration are proportional to the number of emitting transducers. We propose a twofold strategy to accelerate the time-to-solution by identifying the optimal number and location of emitters using sequential optimal experimental design (SOED). SOED is a powerful tool to iteratively add the most informative transducer or remove redundant measurements, respectively. This approach simultaneously provides optimized transducer configurations and a cost-benefit curve that quantifies the information gain versus the computational cost. First, we propose a method to identify the emitters that provide reconstructions with minimal expected uncertainties. Using a Bayesian approach, model uncertainties and resolution can be quantified with the trace of the posterior covariance. By linearizing the wave equation, we can compute the posterior covariance using the inverse of the Gauss-Newton approximation of the Hessian. Furthermore, this posterior is independent of the breast model and the experimental data, thus enabling pre-acquisition experimental optimization. Then, for the post-acquisition inversion, we present an approach to select a subsample of sources that accurately approximates the full gradient direction in each iteration. We control the convergence of the angular differences between consecutive gradient directions by randomly adding new emitters into the subsample. We present synthetic studies in 2D and 3D that consider a ring-shaped and a semi-ellipsoidal scanning device, respectively. Numerical results suggest that the provided methods have the potential to identify redundancies from the corresponding cost-benefit curves. Furthermore, the gradient direction rapidly converges to the direction of the full gradient, which appears to be independent of the model and the emitter locations.