The Research Of Multi-plane Phase Retrievalalgorithm Based On Sparse Representation

Phase retrieval(PR)refers to recover the original signal from the intensity measurement of its Fresnel transform,or of any other linear transform.Since PR is ill-posed,it is feasible to reduce the error caused by the ill-posedness by using multiple observations and the sparse priori of the image.In this paper,we focus on multi-plane phase retrieval algorithm based on image sparse representation.The main contents are as follows:First,utilizing the sparse representation of natural images over Dual-Tree Complex Wavelet Transform,and combining with multiple intensity observations,the paper proposes multi-plane phase retrieval algorithm based on Dual-Tree Complex Wavelet Transform.Separate regularizations for magnitude and phase are constructed to decrease mutual interference.Simulated experiments indicate that the reconstruction effect of the multi-plane phase retrieval algorithm based on Dual-Tree Complex Wavelet Transform is better than the multi-plane phase retrieval algorithm using Tikhonov regularization.Secondly,considering the fact that Dual-Tree Complex Wavelet Transform may lose some low frequency information of an image,it is essential to utilize the sparse representation of natural images over orthogonal DCT with a better energy concentration property because most of the energy of an image concentrates in low frequency part.The paper proposes multi-plane phase retrieval algorithm based on orthogonal DCT dictionary and experiment results show that the multi-plane phase retrieval algorithm based on orthogonal DCT dictionary outperforms the multi-plane phase retrieval algorithm based on Dual-Tree Complex Wavelet Transform.Finally,fixed DCT dictionary is not adaptive due to its fixed atom.To improve the adaptability of dictionary atoms,the paper proposed multi-plane phase retrieval algorithm based on orthogonal dictionary learning.The proposed algorithm can recover the image and learn an orthogonal dictionary that matches the recovered image simultaneously only from the intensity measurements.Due to the fact that the adaptive orthogonal dictionary can capture the image structure,the proposed algorithm can recover the high-quality image only from fewer measurements.Simulated experiments indicate that the proposedmethod outperforms the previous multi-plane PR algorithms in terms of both the objective evaluation and the subjective visual evaluation.Meanwhile,our algorithm is robust to noise.