General expression based inner loop unrolling scheme for TV-GD algorithm adopted in photoacoustic imaging

Although the total variation based gradient descent (TV-GD) algorithm has revealed a good performance for photoacoustic imaging (PAI), fast or real-time imaging remains a challenge. In this paper, the data dependencies that exist in the TV-GD algorithm were exploited, and a general expression was then for the first time derived to unroll the inner loop that occupied the majority of the entire running time of the algorithm. All the terms consisting of the measurement matrices or the under-sampled datasets were then extracted and preprocessed rather than being calculated along with reconstruction. For implementation, we accessed the JACKET toolbox to parallelize the execution of the matrix-vector multiplications and the vector additions generated by the general expression itself. The under-sampled dataset with 30, 60, 90 and 120 projections were adopted to reconstruct a 128×128 Shepp-Logan Phantom. The simulation results revealed a minimum reconstruction time of 0.64s in the case of the 60-view data, and a maximum speedup of 69X from the 120-view dataset.