Breaking the Diffraction Barrier for Passive Sources: Parameter-Decoupled Superresolution Assisted by Physics-Informed Machine Learning

We present a parameter-decoupled superresolution framework for estimating sub-wavelength separations of passive two-point sources without requiring prior knowledge or control of the source. Our theoretical foundation circumvents the need to estimate multiple challenging parameters such as partial coherence, brightness imbalance, random relative phase, and photon statistics. A physics-informed machine learning (ML) model (trained with a standard desktop workstation), synergistically integrating this theory, further addresses practical imperfections including background noise, photon loss, and centroid/orientation misalignment. The integrated parameter-decoupling superresolution method achieves resolution 14 and more times below the diffraction limit (corresponding to ~ 13.5 nm in optical microscopy) on experimentally generated realistic images with >82% fidelity, performance rivaling state-of-the-art techniques for actively controllable sources. Critically, our method's robustness against source parameter variability and source-independent noises enables potential applications in realistic scenarios where source control is infeasible, such as astrophysical imaging, live-cell microscopy, and quantum metrology. This work bridges a critical gap between theoretical superresolution limits and practical implementations for passive systems.

On the Logic Elements Associated with Round-Off Errors and Gaussian Blur in Image Registration: A Simple Case of Commingling

Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions which are subject to blur which is Gaussian or a mixture of Gaussians as well as to round-off errors. Previous approaches address the signal recovery problem as an optimization problem. We focus on a regime with low blur and suggest that the operations of blur, sampling, and quantization are not unlike the operation of a computer program and have an abstraction that can be studied with a type of logic. When the minimum distance between discontinuity points is between $1.5$ and 2 times the sampling interval, we can encounter the simplest form of a type of interference between discontinuity points that we call ``commingling.'' We describe a way to reason about two sets of samples of the same signal that will often result in the correct recovery of signal amplitudes. We also discuss ways to estimate bounds on the distances between discontinuity points.

On Round-Off Errors and Gaussian Blur in Superresolution and in Image Registration

Superresolution theory and techniques seek to recover signals from samples in the presence of blur and noise. Discrete image registration can be an approach to fuse information from different sets of samples of the same signal. Quantization errors in the spatial domain are inherent to digital images. We consider superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions which are subject to blur which is Gaussian or a mixture of Gaussians as well as to round-off errors. We describe a signal-dependent measurement matrix which captures both types of effects. For this setting we show that the difficulties in determining the discontinuity points from two sets of samples even in the absence of other types of noise. If the samples are also subject to statistical noise, then it is necessary to align and segment the data sequences to make the most effective inferences about the amplitudes and discontinuity points. Under some conditions on the blur, the noise, and the distance between discontinuity points, we prove that we can correctly align and determine the first samples following each discontinuity point in two data sequences with an approach based on dynamic programming.

VIPaint: Image Inpainting with Pre-Trained Diffusion Models via Variational Inference

Diffusion probabilistic models learn to remove noise that is artificially added to the data during training. Novel data, like images, may then be generated from Gaussian noise through a sequence of denoising operations. While this Markov process implicitly defines a joint distribution over noise-free data, it is not simple to condition the generative process on masked or partial images. A number of heuristic sampling procedures have been proposed for solving inverse problems with diffusion priors, but these approaches do not directly approximate the true conditional distribution imposed by inference queries, and are often ineffective for large masked regions. Moreover, many of these baselines cannot be applied to latent diffusion models which use image encodings for efficiency. We instead develop a hierarchical variational inference algorithm that analytically marginalizes missing features, and uses a rigorous variational bound to optimize a non-Gaussian Markov approximation of the true diffusion posterior. Through extensive experiments with both pixel-based and latent diffusion models of images, we show that our VIPaint method significantly outperforms previous approaches in both the plausibility and diversity of imputations, and is easily generalized to other inverse problems like deblurring and superresolution.

SuperResolution Radar Gesture Recognitio

"This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible." Driver's interaction with a vehicle via automatic gesture recognition is expected to enhance driving safety by decreasing driver's distraction. Optical and infrared-based gesture recognition systems are limited by occlusions, poor lighting, and varying thermal conditions and, therefore, have limited performance in practical in-cabin applications. Radars are insensitive to lighting or thermal conditions and, therefore, are more suitable for in-cabin applications. However, the spatial resolution of conventional radars is insufficient for accurate gesture recognition. The main objective of this research is to derive an accurate gesture recognition approach using low-resolution radars with deep learning-based super-resolution processing. The main idea is to reconstruct high-resolution information from the radar's low-resolution measurements. The major challenge is the derivation of the real-time processing approach. The proposed approach combines conventional signal processing and deep learning methods. The radar echoes are arranged in 3D data cubes and processed using a super-resolution model to enhance range and Doppler resolution. The FFT is used to generate the range-Doppler maps, which enter the deep neural network for efficient gesture recognition. The preliminary results demonstrated the proposed approach's efficiency in achieving high gesture recognition performance using conventional low-resolution radars.

UTSRMorph: A Unified Transformer and Superresolution Network for Unsupervised Medical Image Registration

Complicated image registration is a key issue in medical image analysis, and deep learning-based methods have achieved better results than traditional methods. The methods include ConvNet-based and Transformer-based methods. Although ConvNets can effectively utilize local information to reduce redundancy via small neighborhood convolution, the limited receptive field results in the inability to capture global dependencies. Transformers can establish long-distance dependencies via a self-attention mechanism; however, the intense calculation of the relationships among all tokens leads to high redundancy. We propose a novel unsupervised image registration method named the unified Transformer and superresolution (UTSRMorph) network, which can enhance feature representation learning in the encoder and generate detailed displacement fields in the decoder to overcome these problems. We first propose a fusion attention block to integrate the advantages of ConvNets and Transformers, which inserts a ConvNet-based channel attention module into a multihead self-attention module. The overlapping attention block, a novel cross-attention method, uses overlapping windows to obtain abundant correlations with match information of a pair of images. Then, the blocks are flexibly stacked into a new powerful encoder. The decoder generation process of a high-resolution deformation displacement field from low-resolution features is considered as a superresolution process. Specifically, the superresolution module was employed to replace interpolation upsampling, which can overcome feature degradation. UTSRMorph was compared to state-of-the-art registration methods in the 3D brain MR (OASIS, IXI) and MR-CT datasets. The qualitative and quantitative results indicate that UTSRMorph achieves relatively better performance. The code and datasets are publicly available at https://github.com/Runshi-Zhang/UTSRMorph.

Hyperspectral Spatial Super-Resolution using Keystone Error

Hyperspectral images enable precise identification of ground objects by capturing their spectral signatures with fine spectral resolution.While high spatial resolution further enhances this capability, increasing spatial resolution through hardware like larger telescopes is costly and inefficient. A more optimal solution is using ground processing techniques, such as hypersharpening, to merge high spectral and spatial resolution data. However, this method works best when datasets are captured under similar conditions, which is difficult when using data from different times. In this work, we propose a superresolution approach to enhance hyperspectral data's spatial resolution without auxiliary input. Our method estimates the high-resolution point spread function (PSF) using blind deconvolution and corrects for sampling-related blur using a model-based superresolution framework. This differs from previous approaches by not assuming a known highresolution blur. We also introduce an adaptive prior that improves performance compared to existing methods. Applied to the visible and near-infrared (VNIR) spectrometer of HySIS, ISRO hyperspectral sensor, our algorithm removes aliasing and boosts resolution by approximately 1.3 times. It is versatile and can be applied to similar systems.

EarthGen: Generating the World from Top-Down Views

In this work, we present a novel method for extensive multi-scale generative terrain modeling. At the core of our model is a cascade of superresolution diffusion models that can be combined to produce consistent images across multiple resolutions. Pairing this concept with a tiled generation method yields a scalable system that can generate thousands of square kilometers of realistic Earth surfaces at high resolution. We evaluate our method on a dataset collected from Bing Maps and show that it outperforms super-resolution baselines on the extreme super-resolution task of 1024x zoom. We also demonstrate its ability to create diverse and coherent scenes via an interactive gigapixel-scale generated map. Finally, we demonstrate how our system can be extended to enable novel content creation applications including controllable world generation and 3D scene generation.

Latent-INR: A Flexible Framework for Implicit Representations of Videos with Discriminative Semantics

Implicit Neural Networks (INRs) have emerged as powerful representations to encode all forms of data, including images, videos, audios, and scenes. With video, many INRs for video have been proposed for the compression task, and recent methods feature significant improvements with respect to encoding time, storage, and reconstruction quality. However, these encoded representations lack semantic meaning, so they cannot be used for any downstream tasks that require such properties, such as retrieval. This can act as a barrier for adoption of video INRs over traditional codecs as they do not offer any significant edge apart from compression. To alleviate this, we propose a flexible framework that decouples the spatial and temporal aspects of the video INR. We accomplish this with a dictionary of per-frame latents that are learned jointly with a set of video specific hypernetworks, such that given a latent, these hypernetworks can predict the INR weights to reconstruct the given frame. This framework not only retains the compression efficiency, but the learned latents can be aligned with features from large vision models, which grants them discriminative properties. We align these latents with CLIP and show good performance for both compression and video retrieval tasks. By aligning with VideoLlama, we are able to perform open-ended chat with our learned latents as the visual inputs. Additionally, the learned latents serve as a proxy for the underlying weights, allowing us perform tasks like video interpolation. These semantic properties and applications, existing simultaneously with ability to perform compression, interpolation, and superresolution properties, are a first in this field of work.

Autoencoders in Function Space

Autoencoders have found widespread application, in both their original deterministic form and in their variational formulation (VAEs). In scientific applications it is often of interest to consider data that are comprised of functions; the same perspective is useful in image processing. In practice, discretisation (of differential equations arising in the sciences) or pixellation (of images) renders problems finite dimensional, but conceiving first of algorithms that operate on functions, and only then discretising or pixellating, leads to better algorithms that smoothly operate between different levels of discretisation or pixellation. In this paper function-space versions of the autoencoder (FAE) and variational autoencoder (FVAE) are introduced, analysed, and deployed. Well-definedness of the objective function governing VAEs is a subtle issue, even in finite dimension, and more so on function space. The FVAE objective is well defined whenever the data distribution is compatible with the chosen generative model; this happens, for example, when the data arise from a stochastic differential equation. The FAE objective is valid much more broadly, and can be straightforwardly applied to data governed by differential equations. Pairing these objectives with neural operator architectures, which can thus be evaluated on any mesh, enables new applications of autoencoders to inpainting, superresolution, and generative modelling of scientific data.