Abstract: A novel algorithm, namely iterative de-noising shrinkage-thresholding (IDNST) algorithm, is presented to reconstruct the original image from digital holography in a compressed sensing framework. The proposed algorithm can reduce the computational complexity in classical digital holography process, as well as the data in transmission. The proposed algorithm adopts two new factors, i.e., the de-noising iteration factor and the shrinkage factor of regularization. Furthermore, the proposed algorithm obtains a new iterative value using the previously updated iterative values, the iteration factor and the shrinking regularization parameter. This improves the convergence speed and the reconstruction accuracy. Simulation results show that the original image can be reconstructed from the digital hologram perfectly with high probability by the IDNST algorithm.

Key words: compressed sensing, digital holography, sparse representation of hologram, measurement matrix, iterative de-noising shrinkage-thresholding algorithm (IDNST)