This study investigates the application of Super-Resolution techniques in holographic microscopy to enhance quantitative phase imaging. An off-axis Mach-Zehnder interferometric setup was employed to capture interferograms. The study evaluates two Super-Resolution models, RCAN and Real-ESRGAN, for their effectiveness in reconstructing high-resolution interferograms from a microparticle-based dataset. The models were assessed using two primary approaches: image-based analysis for structural detail enhancement and morphological evaluation for maintaining sample integrity and phase map accuracy. The results demonstrate that RCAN achieves superior numerical precision, making it ideal for applications requiring highly accurate phase map reconstruction, while Real-ESRGAN enhances visual quality and structural coherence, making it suitable for visualization-focused applications. This study highlights the potential of Super-Resolution models in overcoming diffraction-imposed resolution limitations in holographic microscopy, opening the way for improved imaging techniques in biomedical diagnostics, materials science, and other high-precision fields.

Deep neural network models can be used to learn complex dynamics from data and reconstruct sparse or noisy signals, thereby accelerating and augmenting experimental measurements. Evaluating the quantum optical properties of solid-state single-photon emitters is a time-consuming task that typically requires interferometric photon correlation experiments, such as Photon correlation Fourier spectroscopy (PCFS) which measures time-resolved single emitter lineshapes. Here, we demonstrate a latent neural ordinary differential equation model that can forecast a complete and noise-free PCFS experiment from a small subset of noisy correlation functions. By encoding measured photon correlations into an initial value problem, the NODE can be propagated to an arbitrary number of interferometer delay times. We demonstrate this with 10 noisy photon correlation functions that are used to extrapolate an entire de-noised interferograms of up to 200 stage positions, enabling up to a 20-fold speedup in experimental acquisition time from $\sim$3 hours to 10 minutes. Our work presents a new approach to greatly accelerate the experimental characterization of novel quantum emitter materials using deep learning.

In recent years, neural networks have been used to solve phase retrieval problems in imaging with superior accuracy and speed than traditional techniques, especially in the presence of noise. However, in the context of interferometric imaging, phase noise has been largely unaddressed by existing neural network architectures. Such noise arises naturally in an interferometer due to mechanical instabilities or atmospheric turbulence, limiting measurement acquisition times and posing a challenge in scenarios with limited light intensity, such as remote sensing. Here, we introduce a 3D-2D Phase Retrieval U-Net (PRUNe) that takes noisy and randomly phase-shifted interferograms as inputs, and outputs a single 2D phase image. A 3D downsampling convolutional encoder captures correlations within and between frames to produce a 2D latent space, which is upsampled by a 2D decoder into a phase image. We test our model against a state-of-the-art singular value decomposition algorithm and find PRUNe reconstructions consistently show more accurate and smooth reconstructions, with a x2.5 - 4 lower mean squared error at multiple signal-to-noise ratios for interferograms with low (< 1 photon/pixel) and high (~100 photons/pixel) signal intensity. Our model presents a faster and more accurate approach to perform phase retrieval in extremely low light intensity interferometry in presence of phase noise, and will find application in other multi-frame noisy imaging techniques.

However, their performance relative to non-natural images, like radar-based satellite data, remains largely unknown. Generating large amounts of synthetic (and especially labelled) satellite data is crucial to implement deep-learning approaches for the processing and analysis of (interferometric) satellite aperture radar data. Here, we leverage PDMs to generate several radarbased satellite image datasets. We show that PDMs succeed in generating images with complex and realistic structures, but that sampling time remains an issue. Indeed, accelerated sampling strategies, which work well on simple image datasets like MNIST, fail on our radar datasets. Probabilistic Diffusion Models (PDMs) are a recent family of deep generative models which have demonstrated state-of-the-art performance in image translation [e.g., SWB21] and generation [e.g., DN21, MFNK In addition, PDMs have the major advantage of being very versatile. They are less prompt to various failures often encountered with other generative approaches, such as mode collapse during the training of GANs or posterior collapse for VAEs [LTGN19]. Consequently, this considerably reduces the engineering work required to train generative models, and paves the way for fully automated data analysis pipelines in remote sensing.

Single neural networks have achieved simultaneous phase retrieval with aberration compensation and phase unwrapping in off-axis Quantitative Phase Imaging (QPI). However, when designing the phase retrieval neural network architecture, the trade-off between computation latency and accuracy has been largely neglected. Here, we propose Neural Architecture Search (NAS) generated Phase Retrieval Net (NAS-PRNet), which is an encoder-decoder style neural network, automatically found from a large neural network architecture search space. The NAS scheme in NAS-PRNet is modified from SparseMask, in which the learning of skip connections between the encoder and the decoder is formulated as a differentiable NAS problem, and the gradient decent is applied to efficiently search the optimal skip connections. Using MobileNet-v2 as the encoder and a synthesized loss that incorporates phase reconstruction and network sparsity losses, NAS-PRNet has realized fast and accurate phase retrieval of biological cells. When tested on a cell dataset, NAS-PRNet has achieved a Peak Signal-to-Noise Ratio (PSNR) of 36.1 dB, outperforming the widely used U-Net and original SparseMask-generated neural network. Notably, the computation latency of NAS-PRNet is only 31 ms which is 12 times less than U-Net. Moreover, the connectivity scheme in NAS-PRNet, identified from one off-axis QPI system, can be well fitted to another with different fringe patterns.

Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$ and $\pi$ while it is the absolute phase that is required to get a true measurement. There is a long history of methods designed to recover accurately this phase from the phase "wrapped" inside $]-\pi,\pi]$. However, noise and under-sampling limit the effectiveness of most techniques and require highly sophisticated algorithms that can process imperfect measurements. Ultimately, analysing successfully an interferogram amounts to pattern recognition, a task where radial basis function neural networks truly excel at. The proposed neural network is designed to unwrap the phase from two-dimensional interferograms, where aliasing, stemming from under-resolved regions, and noise levels are significant. The neural network can be trained in parallel and in three stages, using gradient-based supervised learning. Parallelism allows to handle relatively large data sets, but requires a supplemental step to synchronized the fully unwrapped phase across the different networks.

Earth's physical properties like atmosphere, topography and ground instability can be determined by differencing billions of phase measurements (pixels) in subsequent matching Interferometric Synthetic Aperture Radar (InSAR) images. Quality (coherence) of each pixel can vary from perfect information (1) to complete noise (0), which needs to be quantified, alongside filtering information-bearing pixels. Phase filtering is thus critical to InSAR's Digital Elevation Model (DEM) production pipeline, as it removes spatial inconsistencies (residues), immensely improving the subsequent unwrapping. Recent explosion in quantity of available InSAR data can facilitate Wide Area Monitoring (WAM) over several geographical regions, if effective and efficient automated processing can obviate manual quality-control. Advances in parallel computing architectures and Convolutional Neural Networks (CNNs) which thrive on them to rival human performance on visual pattern recognition makes this approach ideal for InSAR phase filtering for WAM, but remains largely unexplored. We propose "GenInSAR", a CNN-based generative model for joint phase filtering and coherence estimation. We use satellite and simulated InSAR images to show overall superior performance of GenInSAR over five algorithms qualitatively, and quantitatively using Phase and Coherence Root-Mean-Squared-Error, Residue Reduction Percentage, and Phase Cosine Error.

Interferometric Synthetic Aperture Radar (InSAR) imagery based on microwaves reflected off ground targets is becoming increasingly important in remote sensing for ground movement estimation. However, the reflections are contaminated by noise, which distorts the signal's wrapped phase. Demarcation of image regions based on degree of contamination ("coherence") is an important component of the InSAR processing pipeline. We introduce Convolutional Neural Networks (CNNs) to this problem domain and show their effectiveness in improving coherence-based demarcation and reducing misclassifications in completely incoherent regions through intelligent preprocessing of training data. Quantitative and qualitative comparisons prove superiority of proposed method over three established methods.

-- Interferometric Synthetic Aperture Radar (InSAR) imagery for estimating ground movement, based on micro waves reflected off ground targets is gaining increasing importance in remote sensing. However, noise corrupts microwave reflections received at satellite and contaminates the signal's wrapped phase. We introduce Convolutional Neural Networks (CNNs) to thi s problem domain and show the effectiveness of autoencoder CNN architectures to learn InSAR image denoising filters in the absence of clean ground truth images, and for artefact reduction in estimated coherence through intelligent preprocessing of training data. We compare our results with four established methods to illustrate superiority of proposed method . Remote sensing using activate microwave, especially in t he form of Synthetic Aperture Radar Interferometry (InSAR), has been extensively used in decades .

In multi-temporal SAR interferometry (MT-InSAR), persistent scatterer (PS) pixels are used to estimate geophysical parameters, essentially deformation. Conventionally, PS pixels are selected on the basis of the estimated noise present in the spatially uncorrelated phase component along with look-angle error in a temporal interferometric stack. In this study, two deep learning architectures, namely convolutional neural network for interferometric semantic segmentation (CNN-ISS) and convolutional long short term memory network for interferometric semantic segmentation (CLSTM-ISS), based on learning spatial and spatio-temporal behaviour respectively, were proposed for selection of PS pixels. These networks were trained to relate the interferometric phase history to its classification into phase stable (PS) and phase unstable (non-PS) measurement pixels using ~10,000 real world interferometric images of different study sites containing man-made objects, forests, vegetation, uncropped land, water bodies, and areas affected by lengthening, foreshortening, layover and shadowing. The networks were trained using training labels obtained from the Stanford method for Persistent Scatterer Interferometry (StaMPS) algorithm. However, pixel selection results, when compared to a combination of R-index and a classified image of the test dataset, reveal that CLSTM-ISS estimates improved the classification of PS and non-PS pixels compared to those of StaMPS and CNN-ISS. The predicted results show that CLSTM-ISS reached an accuracy of 93.50%, higher than that of CNN-ISS (89.21%). CLSTM-ISS also improved the density of reliable PS pixels compared to StaMPS and CNN-ISS and outperformed StaMPS and other conventional MT-InSAR methods in terms of computational efficiency.