With the advent of surveys like Euclid and Vera C. Rubin, astrophysicists will have access to both deep, high-resolution images and multiband images. However, these two types are not simultaneously available in any single dataset. It is therefore vital to devise image deconvolution algorithms that exploit the best of both worlds and that can jointly analyze datasets spanning a range of resolutions and wavelengths. In this work we introduce a novel multiband deconvolution technique aimed at improving the resolution of ground-based astronomical images by leveraging higher-resolution space-based observations. The method capitalizes on the fortunate fact that the Rubin $r$, $i$, and $z$ bands lie within the Euclid VIS band. The algorithm jointly de-convolves all the data to convert the $r$-, $i$-, and $z$-band Rubin images to the resolution of Euclid by leveraging the correlations between the different bands. We also investigate the performance of deep-learning-based denoising with DRUNet to further improve the results. We illustrate the effectiveness of our method in terms of resolution and morphology recovery, flux preservation, and generalization to different noise levels. This approach extends beyond the specific Euclid-Rubin combination, offering a versatile solution to improving the resolution of ground-based images in multiple photometric bands by jointly using any space-based images with overlapping filters.
This work aims to reconstruct image sequences with Total Variation regularity in super-resolution. We consider, in particular, images of scenes for which the point-to-point image transformation is a plane projective transformation. We first describe the super-resolution image's imaging observation model, an interpolation and Fusion estimator, and Projection on Convex Sets. We explain motion and compute the optical flow of a sequence of images using the Horn-Shunck algorithm to estimate motion. We then propose a Total Variation regulazer via a Majorization-Minimization approach to obtain a suitable result. Super Resolution restoration from motion measurements is also discussed. Finally, the simulation's part demonstrates the power of the proposed methodology. As expected, this model does not give real-time results, as seen in the numerical experiments section, but it is the cornerstone for future approaches. Finally, the simulation's part demonstrates the power of the proposed methodology. As expected, this model does not give real-time results, as seen in the numerical experiments section, but it is the cornerstone for future approaches.
As the density of spacecraft in Earth's orbit increases, their recognition, pose and trajectory identification becomes crucial for averting potential collisions and executing debris removal operations. However, training models able to identify a spacecraft and its pose presents a significant challenge due to a lack of available image data for model training. This paper puts forth an innovative framework for generating realistic synthetic datasets of Resident Space Object (RSO) imagery. Using the International Space Station (ISS) as a test case, it goes on to combine image regression with image restoration methodologies to estimate pose from blurred images. An analysis of the proposed image recovery and regression techniques was undertaken, providing insights into the performance, potential enhancements and limitations when applied to real imagery of RSOs. The image recovery approach investigated involves first applying image deconvolution using an effective point spread function, followed by detail object extraction with a U-Net. Interestingly, using only U-Net for image reconstruction the best pose performance was attained, reducing the average Mean Squared Error in image recovery by 97.28% and the average angular error by 71.9%. The successful application of U-Net image restoration combined with the Resnet50 regression network for pose estimation of the International Space Station demonstrates the value of a diverse set of evaluation tools for effective solutions to real-world problems such as the analysis of distant objects in Earth's orbit.
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the detected partitioning. In this paper, we provide theoretical results that permits us to build 2D empirical wavelet filters based on an arbitrary partitioning of the frequency domain. We also propose an algorithm to detect such partitioning from an image spectrum by combining a scale-space representation to estimate the position of dominant harmonic modes and a watershed transform to find the boundaries of the different supports making the expected partition. This whole process allows us to define the empirical watershed wavelet transform. We illustrate the effectiveness and the advantages of such adaptive transform, first visually on toy images, and next on both unsupervised texture segmentation and image deconvolution applications.
Blind image deconvolution (BID) is a classic yet challenging problem in the field of image processing. Recent advances in deep image prior (DIP) have motivated a series of DIP-based approaches, demonstrating remarkable success in BID. However, due to the high non-convexity of the inherent optimization process, these methods are notorious for their sensitivity to the initialized kernel. To alleviate this issue and further improve their performance, we propose a new framework for BID that better considers the prior modeling and the initialization for blur kernels, leveraging a deep generative model. The proposed approach pre-trains a generative adversarial network-based kernel generator that aptly characterizes the kernel priors and a kernel initializer that facilitates a well-informed initialization for the blur kernel through latent space encoding. With the pre-trained kernel generator and initializer, one can obtain a high-quality initialization of the blur kernel, and enable optimization within a compact latent kernel manifold. Such a framework results in an evident performance improvement over existing DIP-based BID methods. Extensive experiments on different datasets demonstrate the effectiveness of the proposed method.
Deep-learning (DL)-based image deconvolution (ID) has exhibited remarkable recovery performance, surpassing traditional linear methods. However, unlike traditional ID approaches that rely on analytical properties of the point spread function (PSF) to achieve high recovery performance - such as specific spectrum properties or small conditional numbers in the convolution matrix - DL techniques lack quantifiable metrics for evaluating PSF suitability for DL-assisted recovery. Aiming to enhance deconvolution quality, we propose a metric that employs a non-linear approach to learn the invertibility of an arbitrary PSF using a neural network by mapping it to a unit impulse. A lower discrepancy between the mapped PSF and a unit impulse indicates a higher likelihood of successful inversion by a DL network. Our findings reveal that this metric correlates with high recovery performance in DL and traditional methods, thereby serving as an effective regularizer in deconvolution tasks. This approach reduces the computational complexity over conventional condition number assessments and is a differentiable process. These useful properties allow its application in designing diffractive optical elements through end-to-end (E2E) optimization, achieving invertible PSFs, and outperforming the E2E baseline framework.
The study of astronomical phenomena through ground-based observations is always challenged by the distorting effects of Earth's atmosphere. Traditional methods of post-facto image correction, essential for correcting these distortions, often rely on simplifying assumptions that limit their effectiveness, particularly in the presence of spatially variant atmospheric turbulence. Such cases are often solved by partitioning the field-of-view into small patches, deconvolving each patch independently, and merging all patches together. This approach is often inefficient and can produce artifacts. Recent advancements in computational techniques and the advent of deep learning offer new pathways to address these limitations. This paper introduces a novel framework leveraging a deep neural network to emulate spatially variant convolutions, offering a breakthrough in the efficiency and accuracy of astronomical image deconvolution. By training on a dataset of images convolved with spatially invariant point spread functions and validating its generalizability to spatially variant conditions, this approach presents a significant advancement over traditional methods. The convolution emulator is used as a forward model in a multi-object multi-frame blind deconvolution algorithm for solar images. The emulator enables the deconvolution of solar observations across large fields of view without resorting to patch-wise mosaicking, thus avoiding artifacts associated with such techniques. This method represents a significant computational advantage, reducing processing times by orders of magnitude.
As ground-based all-sky astronomical surveys will gather millions of images in the coming years, a critical requirement emerges for the development of fast deconvolution algorithms capable of efficiently improving the spatial resolution of these images. By successfully recovering clean and high-resolution images from these surveys, the objective is to deepen the understanding of galaxy formation and evolution through accurate photometric measurements. We introduce a two-step deconvolution framework using a Swin Transformer architecture. Our study reveals that the deep learning-based solution introduces a bias, constraining the scope of scientific analysis. To address this limitation, we propose a novel third step relying on the active coefficients in the sparsity wavelet framework. We conducted a performance comparison between our deep learning-based method and Firedec, a classical deconvolution algorithm, based on an analysis of a subset of the EDisCS cluster samples. We demonstrate the advantage of our method in terms of resolution recovery, generalisation to different noise properties, and computational efficiency. The analysis of this cluster sample not only allowed us to assess the efficiency of our method, but it also enabled us to quantify the number of clumps within these galaxies in relation to their disc colour. This robust technique that we propose holds promise for identifying structures in the distant universe through ground-based images.
Blind deconvolution is an ill-posed problem arising in various fields ranging from microscopy to astronomy. The ill-posed nature of the problem requires adequate priors to arrive to a desirable solution. Recently, it has been shown that deep learning architectures can serve as an image generation prior during unsupervised blind deconvolution optimization, however often exhibiting a performance fluctuation even on a single image. We propose to use Wiener-deconvolution to guide the image generator during optimization by providing it a sharpened version of the blurry image using an auxiliary kernel estimate starting from a Gaussian. We observe that the high-frequency artifacts of deconvolution are reproduced with a delay compared to low-frequency features. In addition, the image generator reproduces low-frequency features of the deconvolved image faster than that of a blurry image. We embed the computational process in a constrained optimization framework and show that the proposed method yields higher stability and performance across multiple datasets. In addition, we provide the code.
We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics relying either on the prior knowledge of reference data and/or on some (partial) knowledge on the noise statistics, the proposed approach optimizes the whiteness of the residual between the observed data and the observation model with no need of ground-truth data.We validate the approach on standard Total Variation-regularized image deconvolution problems which show that the proposed quality metric provides estimates close to the mean-square error oracle and to discrepancy-based principles.
In the imaging process of an astronomical telescope, the deconvolution of its beam or Point Spread Function (PSF) is a crucial task. However, deconvolution presents a classical and challenging inverse computation problem. In scenarios where the beam or PSF is complex or inaccurately measured, such as in interferometric arrays and certain radio telescopes, the resultant blurry images are often challenging to interpret visually or analyze using traditional physical detection methods. We argue that traditional methods frequently lack specific prior knowledge, thereby leading to suboptimal performance. To address this issue and achieve image deconvolution and reconstruction, we propose an unsupervised network architecture that incorporates prior physical information. The network adopts an encoder-decoder structure while leveraging the telescope's PSF as prior knowledge. During network training, we introduced accelerated Fast Fourier Transform (FFT) convolution to enable efficient processing of high-resolution input images and PSFs. We explored various classic regression networks, including autoencoder (AE) and U-Net, and conducted a comprehensive performance evaluation through comparative analysis.
Machine vision is susceptible to laser dazzle, where intense laser light can blind and distort its perception of the environment through oversaturation or permanent damage to sensor pixels. Here we employ a wavefront-coded phase mask to diffuse the energy of laser light and introduce a sandwich generative adversarial network (SGAN) to restore images from complex image degradations, such as varying laser-induced image saturation, mask-induced image blurring, unknown lighting conditions, and various noise corruptions. The SGAN architecture combines discriminative and generative methods by wrapping two GANs around a learnable image deconvolution module. In addition, we make use of Fourier feature representations to reduce the spectral bias of neural networks and improve its learning of high-frequency image details. End-to-end training includes the realistic physics-based synthesis of a large set of training data from publicly available images. We trained the SGAN to suppress the peak laser irradiance as high as $10^6$ times the sensor saturation threshold - the point at which camera sensors may experience damage without the mask. The trained model was evaluated on both a synthetic data set and data collected from the laboratory. The proposed image restoration model quantitatively and qualitatively outperforms state-of-the-art methods for a wide range of scene contents, laser powers, incident laser angles, ambient illumination strengths, and noise characteristics.
In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling-based deep network design since many traditional model-based approaches rely on iterative optimization. Despite exciting progress, typical unrolling approaches heuristically design layer-specific convolution weights to improve performance. Crucially, convergence properties of the underlying iterative algorithm are lost once layer-specific parameters are learned from training data. We propose an unrolling technique that breaks the trade-off between retaining algorithm properties while simultaneously enhancing performance. We focus on image deblurring and unrolling the widely-applied Half-Quadratic Splitting (HQS) algorithm. We develop a new parametrization scheme which enforces layer-specific parameters to asymptotically approach certain fixed points. Through extensive experimental studies, we verify that our approach achieves competitive performance with state-of-the-art unrolled layer-specific learning and significantly improves over the traditional HQS algorithm. We further establish convergence of the proposed unrolled network as the number of layers approaches infinity, and characterize its convergence rate. Our experimental verification involves simulations that validate the analytical results as well as comparison with state-of-the-art non-blind deblurring techniques on benchmark datasets. The merits of the proposed convergent unrolled network are established over competing alternatives, especially in the regime of limited training.
Examining the detailed structure of galaxy populations provides valuable insights into their formation and evolution mechanisms. Significant barriers to such analysis are the non-trivial noise properties of real astronomical images and the point spread function (PSF) which blurs structure. Here we present a framework which combines recent advances in score-based likelihood characterization and diffusion model priors to perform a Bayesian analysis of image deconvolution. The method, when applied to minimally processed \emph{Hubble Space Telescope} (\emph{HST}) data, recovers structures which have otherwise only become visible in next-generation \emph{James Webb Space Telescope} (\emph{JWST}) imaging.
Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves encouraging results in the nonblind deblurring problem. However, since the relationship between images and the network architectures is unclear, it is hard to find a suitable architecture to provide sufficient constraints on the estimated blur kernels and clean images. Also, DIP uses the sparse maximum a posteriori (MAP), which is insufficient to enforce the selection of the recovery image. Recently, variational deep image prior (VDIP) was proposed to impose constraints on both blur kernels and recovery images and take the standard deviation of the image into account during the optimization process by the variational principle. However, we empirically find that VDIP struggles with processing image details and tends to generate suboptimal results when the blur kernel is large. Therefore, we combine total generalized variational (TGV) regularization with VDIP in this paper to overcome these shortcomings of VDIP. TGV is a flexible regularization that utilizes the characteristics of partial derivatives of varying orders to regularize images at different scales, reducing oil painting artifacts while maintaining sharp edges. The proposed VDIP-TGV effectively recovers image edges and details by supplementing extra gradient information through TGV. Additionally, this model is solved by the alternating direction method of multipliers (ADMM), which effectively combines traditional algorithms and deep learning methods. Experiments show that our proposed VDIP-TGV surpasses various state-of-the-art models quantitatively and qualitatively.
Non-blind image deconvolution has been studied for several decades but most of the existing work focuses on blur instead of noise. In photon-limited conditions, however, the excessive amount of shot noise makes traditional deconvolution algorithms fail. In searching for reasons why these methods fail, we present a systematic analysis of the Poisson non-blind deconvolution algorithms reported in the literature, covering both classical and deep learning methods. We compile a list of five "secrets" highlighting the do's and don'ts when designing algorithms. Based on this analysis, we build a proof-of-concept method by combining the five secrets. We find that the new method performs on par with some of the latest methods while outperforming some older ones.
This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. The proposed strategy takes the form of a stochastic relaxed proximal-point iteration that admits two complementary interpretations. For models that are smooth or regularised by Moreau-Yosida smoothing, the algorithm is equivalent to an implicit midpoint discretisation of an overdamped Langevin diffusion targeting the posterior distribution of interest. This discretisation is asymptotically unbiased for Gaussian targets and shown to converge in an accelerated manner for any target that is $\kappa$-strongly log-concave (i.e., requiring in the order of $\sqrt{\kappa}$ iterations to converge, similarly to accelerated optimisation schemes), comparing favorably to [M. Pereyra, L. Vargas Mieles, K.C. Zygalakis, SIAM J. Imaging Sciences, 13,2 (2020), pp. 905-935] which is only provably accelerated for Gaussian targets and has bias. For models that are not smooth, the algorithm is equivalent to a Leimkuhler-Matthews discretisation of a Langevin diffusion targeting a Moreau-Yosida approximation of the posterior distribution of interest, and hence achieves a significantly lower bias than conventional unadjusted Langevin strategies based on the Euler-Maruyama discretisation. For targets that are $\kappa$-strongly log-concave, the provided non-asymptotic convergence analysis also identifies the optimal time step which maximizes the convergence speed. The proposed methodology is demonstrated through a range of experiments related to image deconvolution with Gaussian and Poisson noise, with assumption-driven and data-driven convex priors. Source codes for the numerical experiments of this paper are available from https://github.com/MI2G/accelerated-langevin-imla.
Inverse problems in image reconstruction are fundamentally complicated by unknown noise properties. Classical iterative deconvolution approaches amplify noise and require careful parameter selection for an optimal trade-off between sharpness and grain. Deep learning methods allow for flexible parametrization of the noise and learning its properties directly from the data. Recently, self-supervised blind-spot neural networks were successfully adopted for image deconvolution by including a known point-spread function in the end-to-end training. However, their practical application has been limited to 2D images in the biomedical domain because it implies large kernels that are poorly optimized. We tackle this problem with Fast Fourier Transform convolutions that provide training speed-up in 3D microscopy deconvolution tasks. Further, we propose to adopt a Siamese invariance loss for deconvolution and empirically identify its optimal position in the neural network between blind-spot and full image branches. The experimental results show that our improved framework outperforms the previous state-of-the-art deconvolution methods with a known point spread function.
Radio astronomy is currently thriving with new large ground-based radio telescopes coming online in preparation for the upcoming Square Kilometre Array (SKA). Facilities like LOFAR, MeerKAT/SKA, ASKAP/SKA, and the future SKA-LOW bring tremendous sensitivity in time and frequency, improved angular resolution, and also high-rate data streams that need to be processed. They enable advanced studies of radio transients, volatile by nature, that can be detected or missed in the data. These transients are markers of high-energy accelerations of electrons and manifest in a wide range of temporal scales. Usually studied with dynamic spectroscopy of time series analysis, there is a motivation to search for such sources in large interferometric datasets. This requires efficient and robust signal reconstruction algorithms. To correctly account for the temporal dependency of the data, we improve the classical image deconvolution inverse problem by adding the temporal dependency in the reconstruction problem. Then, we introduce two novel neural network architectures that can do both spatial and temporal modeling of the data and the instrumental response. Then, we simulate representative time-dependent image cubes of point source distributions and realistic telescope pointings of MeerKAT to generate toy models to build the training, validation, and test datasets. Finally, based on the test data, we evaluate the source profile reconstruction performance of the proposed methods and classical image deconvolution algorithm CLEAN applied frame-by-frame. In the presence of increasing noise level in data frame, the proposed methods display a high level of robustness compared to frame-by-frame imaging with CLEAN. The deconvolved image cubes bring a factor of 3 improvement in fidelity of the recovered temporal profiles and a factor of 2 improvement in background denoising.
In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted and learnable regularizers remains largely underexplored. This work aims to justify this combination, by demonstrating that the incorporation of proper handcrafted regularizers alongside learnable regularizers not only reduces the complexity of the learnable prior, but also the performance is notably enhanced. To analyze the impact of this synergy, we introduce the notion of residual structure, to refer to the structure of the solution that cannot be modeled by the handcrafted regularizers per se. Motivated by these, we propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix. Based on the proposed optimization framework, an interpretable model is developed using the deep unrolling strategy, which consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module. Recognizing the collaborative nature of these modules, this work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules. This is facilitated through the incorporation of a proper skip connection, ensuring that essential details and structures identified by other modules are effectively retained and not lost during denoising. Extensive experimental results across simulated and real-world datasets demonstrate that DeepMix is notable for surpassing existing methodologies, offering marked improvements in both image quality and computational efficiency.