Andrés Almansa

Jean Prost, Antoine Houdard, Andrés Almansa et al.

In this paper, we propose to regularize ill-posed inverse problems using a deep hierarchical variational autoencoder (HVAE) as an image prior. The proposed method synthesizes the advantages of i) denoiser-based Plug \& Play approaches and ii) generative model based approaches to inverse problems. First, we exploit VAE properties to design an efficient algorithm that benefits from convergence guarantees of Plug-and-Play (PnP) methods. Second, our approach is not restricted to specialized datasets and the proposed PnP-HVAE model is able to solve image restoration problems on natural images of any size. Our experiments show that the proposed PnP-HVAE method is competitive with both SOTA denoiser-based PnP approaches, and other SOTA restoration methods based on generative models.

Charles Laroche, Andrés Almansa, Matias Tassano

We propose a state-of-the-art method for super-resolution with non-uniform blur. Single-image super-resolution methods seek to restore a high-resolution image from blurred, subsampled, and noisy measurements. Despite their impressive performance, existing techniques usually assume a uniform blur kernel. Hence, these techniques do not generalize well to the more general case of non-uniform blur. Instead, in this paper, we address the more realistic and computationally challenging case of spatially-varying blur. To this end, we first propose a fast deep plug-and-play algorithm, based on linearized ADMM splitting techniques, which can solve the super-resolution problem with spatially-varying blur. Second, we unfold our iterative algorithm into a single network and train it end-to-end. In this way, we overcome the intricacy of manually tuning the parameters involved in the optimization scheme. Our algorithm presents remarkable performance and generalizes well after a single training to a large family of spatially-varying blur kernels, noise levels and scale factors.

Marien Renaud, Jiaming Liu, Valentin de Bortoli et al.

Posterior sampling has been shown to be a powerful Bayesian approach for solving imaging inverse problems. The recent plug-and-play unadjusted Langevin algorithm (PnP-ULA) has emerged as a promising method for Monte Carlo sampling and minimum mean squared error (MMSE) estimation by combining physical measurement models with deep-learning priors specified using image denoisers. However, the intricate relationship between the sampling distribution of PnP-ULA and the mismatched data-fidelity and denoiser has not been theoretically analyzed. We address this gap by proposing a posterior-L2 pseudometric and using it to quantify an explicit error bound for PnP-ULA under mismatched posterior distribution. We numerically validate our theory on several inverse problems such as sampling from Gaussian mixture models and image deblurring. Our results suggest that the sensitivity of the sampling distribution of PnP-ULA to a mismatch in the measurement model and the denoiser can be precisely characterized.

Antoine Monod, Julie Delon, Matias Tassano et al.

This paper presents a novel method for restoring digital videos via a Deep Plug-and-Play (PnP) approach. Under a Bayesian formalism, the method consists in using a deep convolutional denoising network in place of the proximal operator of the prior in an alternating optimization scheme. We distinguish ourselves from prior PnP work by directly applying that method to restore a digital video from a degraded video observation. This way, a network trained once for denoising can be repurposed for other video restoration tasks. Our experiments in video deblurring, super-resolution, and interpolation of random missing pixels all show a clear benefit to using a network specifically designed for video denoising, as it yields better restoration performance and better temporal stability than a single image network with similar denoising performance using the same PnP formulation. Moreover, our method compares favorably to applying a different state-of-the-art PnP scheme separately on each frame of the sequence. This opens new perspectives in the field of video restoration.

Nicolas Cherel, Andrés Almansa, Yann Gousseau et al.

Video inpainting is the task of filling a region in a video in a visually convincing manner. It is very challenging due to the high dimensionality of the data and the temporal consistency required for obtaining convincing results. Recently, diffusion models have shown impressive results in modeling complex data distributions, including images and videos. Such models remain nonetheless very expensive to train and to perform inference with, which strongly reduce their applicability to videos, and yields unreasonable computational loads. We show that in the case of video inpainting, thanks to the highly auto-similar nature of videos, the training data of a diffusion model can be restricted to the input video and still produce very satisfying results. With this internal learning approach, where the training data is limited to a single video, our lightweight models perform very well with only half a million parameters, in contrast to the very large networks with billions of parameters typically found in the literature. We also introduce a new method for efficient training and inference of diffusion models in the context of internal learning, by splitting the diffusion process into different learning intervals corresponding to different noise levels of the diffusion process. We show qualitative and quantitative results, demonstrating that our method reaches or exceeds state of the art performance in the case of dynamic textures and complex dynamic backgrounds

Charles Laroche, Andrés Almansa, Eva Coupeté et al.

Plug & Play methods combine proximal algorithms with denoiser priors to solve inverse problems. These methods rely on the computability of the proximal operator of the data fidelity term. In this paper, we propose a Plug & Play framework based on linearized ADMM that allows us to bypass the computation of intractable proximal operators. We demonstrate the convergence of the algorithm and provide results on restoration tasks such as super-resolution and deblurring with non-uniform blur.

Alessio Spagnoletti, Jean Prost, Andrés Almansa et al.

Text-to-image latent diffusion models (LDMs) have recently emerged as powerful generative models with great potential for solving inverse problems in imaging. However, leveraging such models in a Plug & Play (PnP), zero-shot manner remains challenging because it requires identifying a suitable text prompt for the unknown image of interest. Also, existing text-to-image PnP approaches are highly computationally expensive. We herein address these challenges by proposing a novel PnP inference paradigm specifically designed for embedding generative models within stochastic inverse solvers, with special attention to Latent Consistency Models (LCMs), which distill LDMs into fast generators. We leverage our framework to propose LAtent consisTency INverse sOlver (LATINO), the first zero-shot PnP framework to solve inverse problems with priors encoded by LCMs. Our conditioning mechanism avoids automatic differentiation and reaches SOTA quality in as little as 8 neural function evaluations. As a result, LATINO delivers remarkably accurate solutions and is significantly more memory and computationally efficient than previous approaches. We then embed LATINO within an empirical Bayesian framework that automatically calibrates the text prompt from the observed measurements by marginal maximum likelihood estimation. Extensive experiments show that prompt self-calibration greatly improves estimation, allowing LATINO with PRompt Optimization to define new SOTAs in image reconstruction quality and computational efficiency. The code is available at https://latino-pro.github.io

Jean Prost, Antoine Houdard, Andrés Almansa et al.

We investigate the problem of producing diverse solutions to an image super-resolution problem. From a probabilistic perspective, this can be done by sampling from the posterior distribution of an inverse problem, which requires the definition of a prior distribution on the high-resolution images. In this work, we propose to use a pretrained hierarchical variational autoencoder (HVAE) as a prior. We train a lightweight stochastic encoder to encode low-resolution images in the latent space of a pretrained HVAE. At inference, we combine the low-resolution encoder and the pretrained generative model to super-resolve an image. We demonstrate on the task of face super-resolution that our method provides an advantageous trade-off between the computational efficiency of conditional normalizing flows techniques and the sample quality of diffusion based methods.

Guillermo Carbajal, Andrés Almansa, Pablo Musé

Motion blur caused by camera shake, particularly under large or rotational movements, remains a major challenge in image restoration. We propose a deep learning framework that jointly estimates the latent sharp image and the underlying camera motion trajectory from a single blurry image. Our method leverages the Projective Motion Blur Model (PMBM), implemented efficiently using a differentiable blur creation module compatible with modern networks. A neural network predicts a full 3D rotation trajectory, which guides a model-based restoration network trained end-to-end. This modular architecture provides interpretability by revealing the camera motion that produced the blur. Moreover, this trajectory enables the reconstruction of the sequence of sharp images that generated the observed blurry image. To further refine results, we optimize the trajectory post-inference via a reblur loss, improving consistency between the blurry input and the restored output. Extensive experiments show that our method achieves state-of-the-art performance on both synthetic and real datasets, particularly in cases with severe or spatially variant blur, where end-to-end deblurring networks struggle. Code and trained models are available at https://github.com/GuillermoCarbajal/Blur2Seq/

Nicolas Cherel, Andrés Almansa, Yann Gousseau et al.

Attention mechanisms have become of crucial importance in deep learning in recent years. These non-local operations, which are similar to traditional patch-based methods in image processing, complement local convolutions. However, computing the full attention matrix is an expensive step with heavy memory and computational loads. These limitations curb network architectures and performances, in particular for the case of high resolution images. We propose an efficient attention layer based on the stochastic algorithm PatchMatch, which is used for determining approximate nearest neighbors. We refer to our proposed layer as a "Patch-based Stochastic Attention Layer" (PSAL). Furthermore, we propose different approaches, based on patch aggregation, to ensure the differentiability of PSAL, thus allowing end-to-end training of any network containing our layer. PSAL has a small memory footprint and can therefore scale to high resolution images. It maintains this footprint without sacrificing spatial precision and globality of the nearest neighbors, which means that it can be easily inserted in any level of a deep architecture, even in shallower levels. We demonstrate the usefulness of PSAL on several image editing tasks, such as image inpainting, guided image colorization, and single-image super-resolution. Our code is available at: https://github.com/ncherel/psal

Marcela Carvalho, Bertrand Le Saux, Pauline Trouvé-Peloux et al.

Aerial or satellite imagery is a great source for land surface analysis, which might yield land use maps or elevation models. In this investigation, we present a neural network framework for learning semantics and local height together. We show how this joint multi-task learning benefits to each task on the large dataset of the 2018 Data Fusion Contest. Moreover, our framework also yields an uncertainty map which allows assessing the prediction of the model. Code is available at https://github.com/marcelampc/mtl_aerial_images .

Marcela Carvalho, Bertrand Le Saux, Pauline Trouvé-Peloux et al.

Depth estimation is of critical interest for scene understanding and accurate 3D reconstruction. Most recent approaches in depth estimation with deep learning exploit geometrical structures of standard sharp images to predict corresponding depth maps. However, cameras can also produce images with defocus blur depending on the depth of the objects and camera settings. Hence, these features may represent an important hint for learning to predict depth. In this paper, we propose a full system for single-image depth prediction in the wild using depth-from-defocus and neural networks. We carry out thorough experiments to test deep convolutional networks on real and simulated defocused images using a realistic model of blur variation with respect to depth. We also investigate the influence of blur on depth prediction observing model uncertainty with a Bayesian neural network approach. From these studies, we show that out-of-focus blur greatly improves the depth-prediction network performances. Furthermore, we transfer the ability learned on a synthetic, indoor dataset to real, indoor and outdoor images. For this purpose, we present a new dataset containing real all-focus and defocused images from a Digital Single-Lens Reflex (DSLR) camera, paired with ground truth depth maps obtained with an active 3D sensor for indoor scenes. The proposed approach is successfully validated on both this new dataset and standard ones as NYUv2 or Depth-in-the-Wild. Code and new datasets are available at https://github.com/marcelampc/d3net_depth_estimation

Alessio Spagnoletti, Andrés Almansa, Marcelo Pereyra

Computational imaging methods increasingly rely on powerful generative diffusion models to tackle challenging image restoration tasks. In particular, state-of-the-art zero-shot image inverse solvers leverage distilled text-to-image latent diffusion models (LDMs) to achieve unprecedented accuracy and perceptual quality with high computational efficiency. However, extending these advances to high-definition video restoration remains a significant challenge, due to the need to recover fine spatial detail while capturing subtle temporal dependencies. Consequently, methods that naively apply image-based LDM priors on a frame-by-frame basis often result in temporally inconsistent reconstructions. We address this challenge by leveraging recent advances in Video Consistency Models (VCMs), which distill video latent diffusion models into fast generators that explicitly capture temporal causality. Building on this foundation, we propose LVTINO, the first zero-shot or plug-and-play inverse solver for high definition video restoration with priors encoded by VCMs. Our conditioning mechanism bypasses the need for automatic differentiation and achieves state-of-the-art video reconstruction quality with only a few neural function evaluations, while ensuring strong measurement consistency and smooth temporal transitions across frames. Extensive experiments on a diverse set of video inverse problems show significant perceptual improvements over current state-of-the-art methods that apply image LDMs frame by frame, establishing a new benchmark in both reconstruction fidelity and computational efficiency.

Nicolas Cherel, Andrés Almansa, Yann Gousseau et al.

Diffusion models are now the undisputed state-of-the-art for image generation and image restoration. However, they require large amounts of computational power for training and inference. In this paper, we propose lightweight diffusion models for image inpainting that can be trained on a single image, or a few images. We show that our approach competes with large state-of-the-art models in specific cases. We also show that training a model on a single image is particularly relevant for image acquisition modality that differ from the RGB images of standard learning databases. We show results in three different contexts: texture images, line drawing images, and materials BRDF, for which we achieve state-of-the-art results in terms of realism, with a computational load that is greatly reduced compared to concurrent methods.

Charles Laroche, Andrés Almansa, Eva Coupete

Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the degradation model such as blur kernel. In particular, we designed an algorithm based on the well-known Expectation-Minimization (EM) estimation method and diffusion models. Our method alternates between approximating the expected log-likelihood of the inverse problem using samples drawn from a diffusion model and a maximization step to estimate unknown model parameters. For the maximization step, we also introduce a novel blur kernel regularization based on a Plug \& Play denoiser. Diffusion models are long to run, thus we provide a fast version of our algorithm. Extensive experiments on blind image deblurring demonstrate the effectiveness of our method when compared to other state-of-the-art approaches.

Rémi Laumont, Valentin de Bortoli, Andrés Almansa et al.

Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the literature, from simple ones expressing local properties to more involved ones exploiting image redundancy at a non-local scale. In a departure from explicit modelling, several recent works have proposed and studied the use of implicit priors defined by an image denoising algorithm. This approach, commonly known as Plug & Play (PnP) regularisation, can deliver remarkably accurate results, particularly when combined with state-of-the-art denoisers based on convolutional neural networks. However, the theoretical analysis of PnP Bayesian models and algorithms is difficult and works on the topic often rely on unrealistic assumptions on the properties of the image denoiser. This papers studies maximum-a-posteriori (MAP) estimation for Bayesian models with PnP priors. We first consider questions related to existence, stability and well-posedness, and then present a convergence proof for MAP computation by PnP stochastic gradient descent (PnP-SGD) under realistic assumptions on the denoiser used. We report a range of imaging experiments demonstrating PnP-SGD as well as comparisons with other PnP schemes.

Rémi Laumont, Valentin de Bortoli, Andrés Almansa et al.

Since the seminal work of Venkatakrishnan et al. in 2013, Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive Minimum Mean Square Error (MMSE) or Maximum A Posteriori (MAP) estimators for inverse problems in imaging by combining an explicit likelihood function with a prior that is implicitly defined by an image denoising algorithm. The PnP algorithms proposed in the literature mainly differ in the iterative schemes they use for optimisation or for sampling. In the case of optimisation schemes, some recent works guarantee the convergence to a fixed point, albeit not necessarily a MAP estimate. In the case of sampling schemes, to the best of our knowledge, there is no known proof of convergence. There also remain important open questions regarding whether the underlying Bayesian models and estimators are well defined, well-posed, and have the basic regularity properties required to support these numerical schemes. To address these limitations, this paper develops theory, methods, and provably convergent algorithms for performing Bayesian inference with PnP priors. We introduce two algorithms: 1) PnP-ULA (Unadjusted Langevin Algorithm) for Monte Carlo sampling and MMSE inference; and 2) PnP-SGD (Stochastic Gradient Descent) for MAP inference. Using recent results on the quantitative convergence of Markov chains, we establish detailed convergence guarantees for these two algorithms under realistic assumptions on the denoising operators used, with special attention to denoisers based on deep neural networks. We also show that these algorithms approximately target a decision-theoretically optimal Bayesian model that is well-posed. The proposed algorithms are demonstrated on several canonical problems such as image deblurring, inpainting, and denoising, where they are used for point estimation as well as for uncertainty visualisation and quantification.

Mario González, Andrés Almansa, Pauline Tan

In this work we address the problem of solving ill-posed inverse problems in imaging where the prior is a variational autoencoder (VAE). Specifically we consider the decoupled case where the prior is trained once and can be reused for many different log-concave degradation models without retraining. Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations. The resulting technique (JPMAP) performs Joint Posterior Maximization using an Autoencoding Prior. We show theoretical and experimental evidence that the proposed objective function is quite close to bi-convex. Indeed it satisfies a weak bi-convexity property which is sufficient to guarantee that our optimization scheme converges to a stationary point. We also highlight the importance of correctly training the VAE using a denoising criterion, in order to ensure that the encoder generalizes well to out-of-distribution images, without affecting the quality of the generative model. This simple modification is key to providing robustness to the whole procedure. Finally we show how our joint MAP methodology relates to more common MAP approaches, and we propose a continuation scheme that makes use of our JPMAP algorithm to provide more robust MAP estimates. Experimental results also show the higher quality of the solutions obtained by our JPMAP approach with respect to other non-convex MAP approaches which more often get stuck in spurious local optima.

Jean Prost, Antoine Houdard, Andrés Almansa et al.

In this work, we propose a framework to learn a local regularization model for solving general image restoration problems. This regularizer is defined with a fully convolutional neural network that sees the image through a receptive field corresponding to small image patches. The regularizer is then learned as a critic between unpaired distributions of clean and degraded patches using a Wasserstein generative adversarial networks based energy. This yields a regularization function that can be incorporated in any image restoration problem. The efficiency of the framework is finally shown on denoising and deblurring applications.

Mario González, Andrés Almansa, Mauricio Delbracio et al.

In this paper we address the problem of solving ill-posed inverse problems in imaging where the prior is a neural generative model. Specifically we consider the decoupled case where the prior is trained once and can be reused for many different log-concave degradation models without retraining. Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations. The resulting technique is called JPMAP because it performs Joint Posterior Maximization using an Autoencoding Prior. We show theoretical and experimental evidence that the proposed objective function is quite close to bi-convex. Indeed it satisfies a weak bi-convexity property which is sufficient to guarantee that our optimization scheme converges to a stationary point. Experimental results also show the higher quality of the solutions obtained by our JPMAP approach with respect to other non-convex MAP approaches which more often get stuck in spurious local optima.

Alasdair Newson, Andrés Almansa, Yann Gousseau et al.

Image synthesis is a core problem in modern deep learning, and many recent architectures such as autoencoders and Generative Adversarial networks produce spectacular results on highly complex data, such as images of faces or landscapes. While these results open up a wide range of new, advanced synthesis applications, there is also a severe lack of theoretical understanding of how these networks work. This results in a wide range of practical problems, such as difficulties in training, the tendency to sample images with little or no variability, and generalisation problems. In this paper, we propose to analyse the ability of the simplest generative network, the autoencoder, to encode and decode two simple geometric attributes : size and position. We believe that, in order to understand more complicated tasks, it is necessary to first understand how these networks process simple attributes. For the first property, we analyse the case of images of centred disks with variable radii. We explain how the autoencoder projects these images to and from a latent space of smallest possible dimension, a scalar. In particular, we describe a closed-form solution to the decoding training problem in a network without biases, and show that during training, the network indeed finds this solution. We then investigate the best regularisation approaches which yield networks that generalise well. For the second property, position, we look at the encoding and decoding of Dirac delta functions, also known as `one-hot' vectors. We describe a hand-crafted filter that achieves encoding perfectly, and show that the network naturally finds this filter during training. We also show experimentally that the decoding can be achieved if the dataset is sampled in an appropriate manner.

Cecilia Aguerrebere, Andrés Almansa, Julie Delon et al.

Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an approach is particularly unstable for most inverse problems beyond denoising. In this work, we propose the use of a hyperprior to model image patches, in order to stabilize the estimation procedure. There are two main advantages to the proposed restoration scheme: Firstly it is adapted to diagonal degradation matrices, and in particular to missing data problems (e.g. inpainting of missing pixels or zooming). Secondly it can deal with signal dependent noise models, particularly suited to digital cameras. As such, the scheme is especially adapted to computational photography. In order to illustrate this point, we provide an application to high dynamic range imaging from a single image taken with a modified sensor, which shows the effectiveness of the proposed scheme.

Alasdair Newson, Andrés Almansa, Matthieu Fradet et al.

We propose an automatic video inpainting algorithm which relies on the optimisation of a global, patch-based functional. Our algorithm is able to deal with a variety of challenging situations which naturally arise in video inpainting, such as the correct reconstruction of dynamic textures, multiple moving objects and moving background. Furthermore, we achieve this in an order of magnitude less execution time with respect to the state-of-the-art. We are also able to achieve good quality results on high definition videos. Finally, we provide specific algorithmic details to make implementation of our algorithm as easy as possible. The resulting algorithm requires no segmentation or manual input other than the definition of the inpainting mask, and can deal with a wider variety of situations than is handled by previous work. 1. Introduction. Advanced image and video editing techniques are increasingly common in the image processing and computer vision world, and are also starting to be used in media entertainment. One common and difficult task closely linked to the world of video editing is image and video " inpainting ". Generally speaking, this is the task of replacing the content of an image or video with some other content which is visually pleasing. This subject has been extensively studied in the case of images, to such an extent that commercial image inpainting products destined for the general public are available, such as Photoshop's " Content Aware fill " [1]. However, while some impressive results have been obtained in the case of videos, the subject has been studied far less extensively than image inpainting. This relative lack of research can largely be attributed to high time complexity due to the added temporal dimension. Indeed, it has only very recently become possible to produce good quality inpainting results on high definition videos, and this only in a semi-automatic manner. Nevertheless, high-quality video inpainting has many important and useful applications such as film restoration, professional post-production in cinema and video editing for personal use. For this reason, we believe that an automatic, generic video inpainting algorithm would be extremely useful for both academic and professional communities.

Mariano Tepper, Pablo Musé, Andrés Almansa

Mathematical Morphology proposes to extract shapes from images as connected components of level sets. These methods prove very suitable for shape recognition and analysis. We present a method to select the perceptually significant (i.e., contrasted) level lines (boundaries of level sets), using the Helmholtz principle as first proposed by Desolneux et al. Contrarily to the classical formulation by Desolneux et al. where level lines must be entirely salient, the proposed method allows to detect partially salient level lines, thus resulting in more robust and more stable detections. We then tackle the problem of combining two gestalts as a measure of saliency and propose a method that reinforces detections. Results in natural images show the good performance of the proposed methods.