l1 norm based sparse reconstruction approach to compressed ultrafast photography of velocity interferometer system for any reflector

The one-dimensional velocity interferometer system for any reflector (VISAR) is widely used in inertial confinement fusion (ICF). Compressed ultrafast photography (CUP) is recently combined with VISAR to enable two-dimensional imaging, in which, the time-varied two-dimensional fringe images reconstruction from one image is a challenging problem. In this Letter, a new l 1 norm based sparse reconstruction approach is presented, to the best of our knowledge, in which: (1) fringe images are sparsely represented with a few coefficients over the discrete cosine transformation (DCT) basis; (2) the image reconstruction is formulated as an l 1 norm based sparse coefficients optimization problem; and (3) the two-step iterative shrinkage/threshold algorithm combined with a soft-thresholding operator is proposed to efficiently solve such a problem. Finally, the results show that, compared with the usual method, reconstructed fringe images with clear boundaries and good continuity are obtained. Additionally, the maximum relative error of the velocity is reduced from 14% to 8%, which is a reduction of approximately half.