Fourier ptychographic microscopy with sparse representation

Fourier ptychographic microscopy (FPM) is a novel computational microscopy technique that provides intensity images with both wide field-of-view and high-resolution. By combining ideas from synthetic aperture and phase retrieval, FPM iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to reconstruct a high-resolution complex sample image. Although FPM is able to bypass the space-bandwidth product (SBP) limit of the optical system, it is vulnerable to the various capturing noises and the reconstruction is easy to trap into the local optimum. To efficiently depress the noise and improve the performance of reconstructed high-resolution image, a FPM with sparse representation is proposed in this paper. The cost function of the reconstruction is formulated as a regularized optimization problem, where the data fidelity is constructed based on a maximum likelihood theory, and the regulation term is expressed as a small number of nonzero elements over an appropriate basis for both amplitude and phase of the reconstructed image. The Nash equilibrium is employed to obtain the approximated solution. We validate the proposed method with both simulated and real experimental data. The results show that the proposed method achieves state-of-the-art performance in comparison with other approaches.