Sparsity-regularized coded ptychography for robust and efficient lensless microscopy on a chip

In ptychographic imaging, the trade-off between the number of acquisitions and the resultant imaging quality presents a complex optimization problem. Increasing the number of acquisitions typically yields reconstructions with higher spatial resolution and finer details. Conversely, a reduction in measurement frequency often compromises the quality of the reconstructed images, manifesting as increased noise and coarser details. To address this challenge, we employ sparsity priors to reformulate the ptychographic reconstruction task as a total variation regularized optimization problem. We introduce a new computational framework, termed the ptychographic proximal total-variation (PPTV) solver, designed to integrate into existing ptychography settings without necessitating hardware modifications. Through comprehensive numerical simulations, we validate that PPTV-driven coded ptychography is capable of producing highly accurate reconstructions with a minimal set of eight intensity measurements. Convergence analysis further substantiates the robustness, stability, and computational feasibility of the proposed PPTV algorithm. Experimental results obtained from optical setups unequivocally demonstrate that the PPTV algorithm facilitates high-throughput, high-resolution imaging while significantly reducing the measurement burden. These findings indicate that the PPTV algorithm has the potential to substantially mitigate the resource-intensive requirements traditionally associated with high-quality ptychographic imaging, thereby offering a pathway toward the development of more compact and efficient ptychographic microscopy systems.Comment: 15 pages, 7 figure

Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and outlook on how to better use DL to improve the reliability and efficiency in PR. Furthermore, we present a live-updating resource (https://github.com/kqwang/phase-recovery) for readers to learn more about PR.Comment: 82 pages, 32 figure

Tight-frame-like Sparse Recovery Using Non-tight Sensing Matrices

The choice of the sensing matrix is crucial in compressed sensing (CS). Gaussian sensing matrices possess the desirable restricted isometry property (RIP), which is crucial for providing performance guarantees on sparse recovery. Further, sensing matrices that constitute a Parseval tight frame result in minimum mean-squared-error (MSE) reconstruction given oracle knowledge of the support of the sparse vector. However, if the sensing matrix is not tight, could one achieve the reconstruction performance assured by a tight frame by suitably designing the reconstruction strategy? This is the key question that we address in this paper. We develop a novel formulation that relies on a generalized l2-norm-based data-fidelity loss that tightens the sensing matrix, along with the standard l1 penalty for enforcing sparsity. The optimization is performed using proximal gradient method, resulting in the tight-frame iterative shrinkage thresholding algorithm (TF-ISTA). We show that the objective convergence of TF-ISTA is linear akin to that of ISTA. Incorporating Nesterovs momentum into TF-ISTA results in a faster variant, namely, TF-FISTA, whose objective convergence is quadratic, akin to that of FISTA. We provide performance guarantees on the l2-error for the proposed formulation. Experimental results show that the proposed algorithms offer superior sparse recovery performance and faster convergence. Proceeding further, we develop the network variants of TF-ISTA and TF-FISTA, wherein a convolutional neural network is used as the sparsifying operator. On the application front, we consider compressed sensing image recovery (CSIR). Experimental results on Set11, BSD68, Urban100, and DIV2K datasets show that the proposed models outperform state-of-the-art sparse recovery methods, with performance measured in terms of peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM).Comment: 33 pages, 12 figure

Minimally-Invasive Lens-Free Computational Microendoscopy

Ultra-miniaturized imaging tools are vital for numerous biomedical applications. Such minimally-invasive imagers allow for navigation into hard-to-reach regions and, for example, observation of deep brain activity in freely moving animals with minimal ancillary tissue damage. Conventional solutions employ distal microlenses. However, as lenses become smaller and thus less invasive they develop greater optical aberrations, requiring bulkier compound designs with restricted field-of-view. In addition, tools capable of 3-dimensional volumetric imaging require components that physically scan the focal plane, which ultimately increases the distal complexity, footprint, and weight. Simply put, minimally-invasive imaging systems have limited information capacity due to their given cross-sectional area. This thesis explores minimally-invasive lens-free microendoscopy enabled by a successful integration of signal processing, optical hardware, and image reconstruction algorithms. Several computational microendoscopy architectures that simultaneously achieve miniaturization and high information content are presented. Leveraging the computational imaging techniques enables color-resolved imaging with wide field-of-view, and 3-dimensional volumetric reconstruction of an unknown scene using a single camera frame without any actuated parts, further advancing the performance versus invasiveness of microendoscopy