General expression based loop unrolling scheme for real-time implementation of PAI

Despite the total variation 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, a dependence graph was introduced to help to exploit the data dependencies that exist in the TV-GD algorithm, 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. Thus all the terms consisting of the system matrices or the projections were extracted and preprocessed rather than being calculated along with reconstruction, and the reconstruction time was then expected to be linear to the iteration steps decided by the outer loop. For implementation, we adopted a low cost preprocessing method to avoid directly calculating the compute-intensive matrix chain products carried by the general expression itself. For simplicity, we accessed the CUBLAS library to parallelize the execution of the matrix-vector multiplication and the vector addition generated by the general expression. The under-sampled data with 30, 60, 90 and 120 projections were adopted to reconstruct a 128×128 Shepp-Logan Phantom. As expected, the simulation results revealed that the reconstruction time of the proposed scheme almost increased linearly with the iteration steps. Similarly, once the iteration steps was determined, the reconstruction time appeared independent of the sampling points and almost kept still. In addition, the mean squared errors (MSEs) of reconstruction were kept lower than 10^-5 in each case with the iteration steps set as 30, and a maximum speedup of 179X was then achieved from the 120-view data with 30 iterations.