The imaging quality of in-line digital holography is challenged by the twin-image and aliasing effects because sensors only respond to intensity and pixels are of finite size. As a result, phase retrieval and pixel super-resolution techniques serve as two essential ingredients for high-fidelity and high-resolution holographic imaging. In this work, we combine the two as a unified optimization problem and propose a generalized algorithmic framework for pixel-super-resolved phase retrieval. In particular, we introduce the iterative projection algorithms and gradient descent algorithms for solving this problem. The basic building blocks, namely the projection operator and the Wirtinger gradient, are derived and analyzed. As an example, the Wirtinger gradient descent algorithm for pixel-super-resolved phase retrieval, termed as Wirtinger-PSR, is proposed and compared with the classical error-reduction algorithm. The Wirtinger-PSR algorithm is verified with both simulated and experimental data. The proposed framework generalizes well to various physical settings and helps bridging the gap between empirical studies and theoretical analyses.
In order to increase signal-to-noise ratio in optical imaging, most detectors sacrifice resolution to increase pixel size in a confined area, which impedes further development of high throughput holographic imaging. Although the pixel super-resolution technique (PSR) enables resolution enhancement, it suffers from the trade-off between reconstruction quality and super-resolution ratio. In this work, we report a high-fidelity PSR phase retrieval method with plug-and-play optimization, termed PNP-PSR. It decomposes PSR reconstruction into independent sub-problems based on generalized alternating projection framework. An alternating projection operator and an enhancing neural network are employed to tackle the measurement fidelity and statistical prior regularization, respectively. PNP-PSR incorporates the advantages of individual operators, achieving both high efficiency and noise robustness. Extensive experiments show that PNP-PSR outperforms the existing techniques in both resolution enhancement and noise suppression.
Holography provides access to the optical phase. The emerging compressive phase retrieval approach can achieve in-line holographic imaging beyond the information-theoretic limit or even from a single shot by exploring the signal priors. However, iterative projection methods based on physical knowledge of the wavefield suffer from poor imaging quality, whereas the regularization techniques sacrifice robustness for fidelity. In this work, we present a unified compressive phase retrieval framework for in-line holography that encapsulates the unique advantages of both physical constraints and sparsity priors. In particular, a constrained complex total variation (CCTV) regularizer is introduced that explores the well-known absorption and support constraints together with sparsity in the gradient domain, enabling practical high-quality in-line holographic imaging from a single intensity image. We developed efficient solvers based on the proximal gradient method for the non-smooth regularized inverse problem and the corresponding denoising subproblem. Theoretical analyses further guarantee the convergence of the algorithms with prespecified parameters, obviating the need for manual parameter tuning. As both simulated and optical experiments demonstrate, the proposed CCTV model can characterize complex natural scenes while utilizing physically tractable constraints for quality enhancement. This new compressive phase retrieval approach can be extended, with minor adjustments, to various imaging configurations, sparsifying operators, and physical knowledge. It may cast new light on both theoretical and empirical studies.
Pixel super-resolution (PSR) techniques have been developed to overcome the sampling limit in lensless digital holographic imaging. However, the inherent non-convexity of the PSR phase retrieval problem can potentially degrade reconstruction quality by causing the iterations to tend toward a false local minimum. Furthermore, the ill posedness of the up-sampling procedure renders PSR algorithms highly susceptible to noise. In this Letter, we propose a heuristic PSR algorithm with adaptive smoothing (AS-PSR) to achieve high-fidelity reconstruction. By automatically adjusting the intensity constraints on the estimated field, the algorithm can effectively locate the optimal solution and converge with high reconstruction quality, pushing the resolution toward the diffraction limit. The proposed method is verified experimentally within a coherent modulation phase retrieval framework, achieving a twofold improvement in resolution. The AS-PSR algorithm can be further applied to other phase retrieval methods based on alternating projection.
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