Accelerating the over-relaxed iterative shrinkage-thresholding algorithms with fast and exact line search for high resolution tomographic image reconstruction

This paper proposes an accelerating process through the use of a fast and exact line search for the over-relaxed monotone fast iterative shrinkage-threshold algorithms (OMFISTA). This algorithm is applied to high resolution tomographic image reconstruction using data from the Brazilian Synchrotron Light Source (LNLS). The LNLS can capture lots of data from the scanned objects in each angle, but in order to reduce acquisition time, only few angles are captured. Due to the reduced angles, the l₁ penalty is used as a prior to provide a proper reconstruction. Algorithms, such as the fast iterative shrinkage-threshold algorithms (FISTA) and the OMFISTA can be used with some success. However, due to the large computational time at each iteration, even with fast projection/backprojection operators, any reduction in the number of iterations is welcome. In this paper, the fast and exact unidimensional optimization for l₂-l₁ is used as line search to accelerate the OMFISTA. The results in this paper illustrate that this line search accelerated OMFISTA is faster than FISTA, MFISTA and the OMFISTA.