Dynamic reconstruction of three-dimensional photoacoustic tomography from few projections

Abstract

Dynamic reconstruction of three-dimensional (3D) photoacoustic tomography (PAT) recovers a sequence of 3D optical contrast distributions and enables to monitor time-varying changes of the chromophore concentrations in biological tissues. To achieve a high frame rate, only a limited-angle few-view (even a single-view) acoustic measurements can be collected at each time frame. These sparse incomplete data represent a formidable challenge to obtain sequences of reconstructed images with both high spatial and temporal resolution. Furthermore, dynamic PAT reconstruction is extremely computationally and memory expensive. High-resolution spatiotemporal reconstruction of 3D objects is, in fact, computationally unfeasible using naïve extensions of classical PAT reconstruction methods for static images. In this study, we present a fast and accurate randomized algorithm for dynamic PAT reconstruction from few tomographic views. Our method is based on the fact that, for many applications of clinical interest, dynamic PAT images are semi-separable in space and time. That is the sequence of PAT images can be expanded using a relatively small number r of basis functions in space and time. Under this assumption, the dynamic PAT reconstruction problem is reformulated as a penalized least squares model, where the nuclear norm of the space-time image is used for the regularization term. By use of a randomized truncated singular value thresholding method, our approach can be implemented in a memory-efficient (only need to store the r spatial and temporal basis functions) and computationally-scalable (only r PAT reconstructions per iteration) manner. The effectiveness of the proposed method is demonstrated using numerical simulation and experimental data of a 3D phantom.