Fig. 6. Recovering high-resolution images with FP and phase retrieval.

The complete recovery algorithm for SAVI is presented on the left side of the figure. A high-resolution estimate of Ψ(u) is recovered by iteratively enforcing intensity measurement constraints in the spatial domain and updating estimates of the spectrum in the Fourier domain. Image denoising is applied every s iterations to suppress the influence of speckle noise in the final reconstruction. Left branch (blue): Traditional FP recovery algorithm used by Ou et al. (18) and Tian et al. (25). Right branch (brown): Image denoising to reduce speckle noise in the estimate of Ψ(u). To illustrate how image recovery improves resolution, a simulation is shown on the right. (A and B) A complex object with an amplitude shown in (A) and having uniformly distributed phase in the range [−π, π] is recorded by a diffraction-limited imaging system (B). (C) FP reduces diffraction blur and speckle size, leading to increased resolution, but still suffers from the presence of speckle and reconstruction artifacts. (D) Incorporating a denoising regularizer in the FP recovery algorithm reduces variation in speckle intensity and reduces the effect of reconstruction artifacts. Brightness in the outsets has been increased to highlight the artifacts. View digitally to see the fine details.