Assessing the quality of automatic image segmentation is crucial in clinical practice, but often very challenging due to the limited availability of ground truth annotations. Reverse Classification Accuracy (RCA) is an approach that estimates the quality of new predictions on unseen samples by training a segmenter on those predictions, and then evaluating it against existing annotated images. In this work we introduce ConfIC-RCA (Conformal In-Context RCA), a novel method for automatically estimating segmentation quality with statistical guarantees in the absence of ground-truth annotations, which consists of two main innovations. First, In-Context RCA, which leverages recent in-context learning models for image segmentation and incorporates retrieval-augmentation techniques to select the most relevant reference images. This approach enables efficient quality estimation with minimal reference data while avoiding the need of training additional models. Second, we introduce Conformal RCA, which extends both the original RCA framework and In-Context RCA to go beyond point estimation. Using tools from split conformal prediction, Conformal RCA produces prediction intervals for segmentation quality providing statistical guarantees that the true score lies within the estimated interval with a user-specified probability. Validated across 10 different medical imaging tasks in various organs and modalities, our methods demonstrate robust performance and computational efficiency, offering a promising solution for automated quality control in clinical workflows, where fast and reliable segmentation assessment is essential. The code is available at https://github.com/mcosarinsky/Conformal-In-Context-RCA.

In recent years, it has become popular to tackle image restoration tasks with a single pretrained diffusion model (DM) and data-fidelity guidance, instead of training a dedicated deep neural network per task. However, such "zero-shot" restoration schemes currently require many Neural Function Evaluations (NFEs) for performing well, which may be attributed to the many NFEs needed in the original generative functionality of the DMs. Recently, faster variants of DMs have been explored for image generation. These include Consistency Models (CMs), which can generate samples via a couple of NFEs. However, existing works that use guided CMs for restoration still require tens of NFEs or fine-tuning of the model per task that leads to performance drop if the assumptions during the fine-tuning are not accurate. In this paper, we propose a zero-shot restoration scheme that uses CMs and operates well with as little as 4 NFEs. It is based on a wise combination of several ingredients: better initialization, back-projection guidance, and above all a novel noise injection mechanism. We demonstrate the advantages of our approach for image super-resolution, deblurring and inpainting. Interestingly, we show that the usefulness of our noise injection technique goes beyond CMs: it can also mitigate the performance degradation of existing guided DM methods when reducing their NFE count. The source code is available at https://github.com/tirer-lab/CM4IR

Recently, it has become popular to tackle image restoration tasks with a single pretrained (unconditional) denoising diffusion model (DDM) and data-fidelity guidance, instead of training a dedicated deep neural network per task. However, such "zero-shot" restoration schemes require many Neural Function Evaluations (NFEs). This follows from the need of iterative schemes with many NFEs already in the original generative functionality of the DDMs. Very recently, faster variants of DDMs have been explored for image generation. A prominent alternative are Consistency Models (CMs), which can generate samples via a couple of NFEs. However, existing works that use guided CMs for restoration still require tens of NFEs or fine-tuning of the model per task. Clearly, the latter is not a zero-shot strategy and, as such, leads to performance drop if the assumptions during the fine-tuning (e.g., the noise level) are not accurate. In this paper, we propose a zero-shot restoration scheme that uses CMs and operates well with as little as 4 NFEs. It is based on a wise combination of several ingredients: better initialization, back-projection guidance, and above all a novel noise injection mechanism. We demonstrate the advantages of our approach for image super-resolution and inpainting.

In many classification applications, the prediction of a deep neural network (DNN) based classifier needs to be accompanied by some confidence indication. Two popular approaches for that aim are: 1) Calibration: modifies the classifier’s softmax values such that the maximal value better estimates the correctness probability; and 2) Conformal Prediction (CP): produces a prediction set of candidate labels that contains the true label with a user-specified probability, guaranteeing marginal coverage but not, e.g., per class coverage. In practice, both types of indications are desirable, yet, so far the interplay between them has not been investigated. Focusing on the ubiquitous Temperature Scaling (TS) calibration, we start this paper with an extensive empirical study of its effect on prominent CP methods. We show that while TS calibration improves the class-conditional coverage of adaptive CP methods, surprisingly, it negatively affects their prediction set sizes. Motivated by this behavior, we explore the effect of TS on CP beyond its calibration application and reveal an intriguing trend under which it allows to trade prediction set size and conditional coverage of adaptive CP methods. Then, we establish a mathematical theory that explains the entire non-monotonic trend. Finally, based on our experiments and theory, we offer guidelines for practitioners to effectively combine adaptive CP with calibration, aligned with user-defined goals.

Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these methods primarily emphasize memory savings, often overlooking potential acceleration in convergence due to their reliance on standard isotropic steepest descent techniques, which can perform suboptimally in the highly anisotropic landscapes typical of deep networks, particularly LLMs. In this paper, we propose SUMO (Subspace-Aware Moment-Orthogonalization), an optimizer that employs exact singular value decomposition (SVD) for moment orthogonalization within a dynamically adapted low-dimensional subspace, enabling norm-inducing steepest descent optimization steps. By explicitly aligning optimization steps with the spectral characteristics of the loss landscape, SUMO effectively mitigates approximation errors associated with commonly used methods like Newton-Schulz orthogonalization approximation. We theoretically establish an upper bound on these approximation errors, proving their dependence on the condition numbers of moments, conditions we analytically demonstrate are encountered during LLM training. Furthermore, we both theoretically and empirically illustrate that exact orthogonalization via SVD substantially improves convergence rates while reducing overall complexity. Empirical evaluations confirm that SUMO accelerates convergence, enhances stability, improves performance, and reduces memory requirements by up to 20\% compared to state-of-the-art methods.

Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a “task-specific” network for each observation model is to use pretrained deep denoisers for imposing only the signal's prior within iterative algorithms, without additional training. Recently, a sampling-based variant of this approach has become popular with the rise of diffusion/score-based generative models. Using denois-ers for general purpose restoration requires guiding the it-erations to ensure agreement of the signal with the observations. In low-noise settings, guidance that is based on back-projection (BP) has been shown to be a promising strat-egy (used recently also under the names “pseudoinverse” or “range/null-space” guidance). However, the presence of noise in the observations hinders the gains from this approach. In this paper, we propose a novel guidance technique, based on preconditioning that allows traversing from BP-based guidance to least squares based guidance along the restoration scheme. The proposed approach is robust to noise while still having much simpler implementation than alternative methods (e.g., it does not require SVD or a large number of iterations). We use it within both an optimization scheme and a sampling-based scheme, and demonstrate its advantages over existing methods for image deblurring and super-resolution.

Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a "task-specific" network for each observation model is to use pretrained deep denoisers for imposing only the signal’s prior within iterative algorithms, without additional training. Recently, this approach has become increasingly popular with the rise of diffusion/score-based generative models, whose core is iterative denoising. Using denoisers for general purpose restoration requires guiding the iterations to ensure agreement of the signal with the observations. In low-noise settings, guidance that is based on back-projection (BP) has been shown to be a promising strategy (used recently in the context of diffusion models also under the names "pseudoinverse" or "range/null-space" guidance). However, the presence of noise in the observations hinders the gains from this approach. In this paper, we propose a novel guidance technique, based on preconditioning that allows traversing from BP-based guidance to least squares based guidance along the restoration scheme. The proposed approach is robust to noise while still having much simpler implementation than alternative methods (e.g., no SVD is required). We demonstrate its advantages for image deblurring and super-resolution.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on node-wise classification, illustrated with community detection on stochastic block model graphs, and explore the feature evolution through the lens of the "Neural Collapse" (NC) phenomenon. When training instance-wise deep classifiers (e.g. for image classification) beyond the zero training error point, NC demonstrates a reduction in the deepest features' within-class variability and an increased alignment of their class means to certain symmetric structures. We start with an empirical study that shows that a decrease in within-class variability is also prevalent in the node-wise classification setting, however, not to the extent observed in the instance-wise case. Then, we theoretically study this distinction. Specifically, we show that even an "optimistic" mathematical model requires that the graphs obey a strict structural condition in order to possess a minimizer with exact collapse. Furthermore, by studying the gradient dynamics of this model, we provide reasoning for the partial collapse observed empirically. Finally, we present a study on the evolution of within- and between-class feature variability across layers of a well-trained GNN and contrast the behavior with spectral methods.

The modern strategy for training deep neural networks for classification tasks includes optimizing the network’s weights even after the training error vanishes to further push the training loss toward zero. Recently, a phenomenon termed “neural collapse" (NC) has been empirically observed in this training procedure. Specifically, it has been shown that the learned features (the output of the penultimate layer) of within-class samples converge to their mean, and the means of different classes exhibit a certain tight frame structure, which is also aligned with the last layer’s weights. Recent papers have shown that minimizers with this structure emerge when optimizing a simplified “unconstrained features model" (UFM) with a regularized cross-entropy loss. In this paper, we further analyze and extend the UFM. First, we study the UFM for the regularized MSE loss, and show that the minimizers’ features can have a more delicate structure than in the cross-entropy case. This affects also the structure of the weights. Then, we extend the UFM by adding another layer of weights as well as ReLU nonlinearity to the model and generalize our previous results. Finally, we empirically demonstrate the usefulness of our nonlinear extended UFM in modeling the NC phenomenon that occurs with practical networks.

Ill-posed inverse problems appear in many image processing applications, such as deblurring and super-resolution. In recent years, solutions that are based on deep Convolutional Neural Networks (CNNs) have shown great promise. Yet, most of these techniques, which train CNNs using external data, are restricted to the observation models that have been used in the training phase. A recent alternative that does not have this drawback relies on learning the target image using internal learning. One such prominent example is the Deep Image Prior (DIP) technique that trains a network directly on the input image with the least-squares loss. In this paper, we propose a new image restoration framework that is based on minimizing a loss function that includes a "projected-version" of the Generalized Stein Unbiased Risk Estimator (GSURE) and parameterization of the latent image by a CNN. We propose two ways to use our framework. In the first one, where no explicit prior is used, we show that the proposed approach outperforms other internal learning methods, such as DIP. In the second one, we show that our GSURE-based loss leads to improved performance when used within a plug-and-play priors scheme.

Estimating the directions of arrival (DOAs) of multiple sources from a single snapshot obtained by a coherent antenna array is a well-known problem, which can be addressed by sparse signal reconstruction methods, where the DOAs are estimated from the peaks of the recovered high-dimensional signal. In this paper, we consider a more challenging DOA estimation task where the array is composed of non-coherent sub-arrays (i.e., sub-arrays that observe different unknown phase shifts due to using low-cost unsynchronized local oscillators). We formulate this problem as the reconstruction of a joint sparse and low-rank matrix and solve its convex relaxation. While the DOAs can be estimated from the solution of the convex problem, we further show how an improvement is obtained if, instead, one estimates from this solution only the phase shifts, creates "phase-corrected" observations and applies another final (plain, coherent) sparsity-based DOA estimation. Numerical experiments show that the proposed approach outperforms strategies that are based on non-coherent processing of the sub-arrays as well as other sparsity-based methods.

The vast majority of image recovery tasks are ill-posed problems. As such, methods that are based on optimization use cost functions that consist of both fidelity and prior (regularization) terms. A recent line of works imposes the prior by the Regularization by Denoising (RED) approach, which exploits the good performance of existing image denoising engines. Yet, the relation of RED to explicit prior terms is still not well understood, as previous work requires too strong assumptions on the denoisers. In this paper, we make two contributions. First, we show that the RED gradient can be seen as a (sub)gradient of a prior function—but taken at a denoised version of the point. As RED is typically applied with a relatively small noise level, this interpretation indicates a similarity between RED and traditional gradients. This leads to our second contribution: We propose to combine RED with the Back-Projection (BP) fidelity term rather than the common Least Squares (LS) term that is used in previous works. We show that the advantages of BP over LS for image deblurring and super-resolution, which have been demonstrated for traditional gradients, carry on to the RED approach.

Ill-posed linear inverse problems appear in many scientific setups and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection (BP) based fidelity term as an alternative to the common least squares (LS) and demonstrated excellent results for popular inverse problems. These works have also empirically shown that using the BP term, rather than the LS term, requires fewer iterations of optimization algorithms. In this paper, we examine the convergence rate of the projected gradient descent algorithm for the BP objective. Our analysis allows us to identify an inherent source for its faster convergence compared to using the LS objective, while making only mild assumptions. We also analyze the more general proximal gradient method under a relaxed contraction condition on the proximal mapping of the prior. This analysis further highlights the advantage of BP when the linear measurement operator is badly conditioned. Numerical experiments with both $\ell_1$-norm and GAN based priors corroborate our theoretical results.

In the recent years, there has been a significant improvement in the quality of samples produced by (deep) generative models such as variational auto-encoders and generative adversarial networks. However, the representation capabilities of these methods still do not capture the full distribution for complex classes of images, such as human faces. This deficiency has been clearly observed in previous works that use pre-trained generative models to solve imaging inverse problems. In this paper, we suggest to mitigate the limited representation capabilities of generators by making them image-adaptive and enforcing compliance of the restoration with the observations via back-projections. We empirically demonstrate the advantages of our proposed approach for image super-resolution and compressed sensing.

The single image super-resolution task is one of the most examined inverse problems in the past decade. In the recent years, Deep Neural Networks (DNNs) have shown superior performance over alternative methods when the acquisition process uses a fixed known downscaling kernel---typically a bicubic kernel. However, several recent works have shown that in practical scenarios, where the test data mismatch the training data (e.g. when the downscaling kernel is not the bicubic kernel or is not available at training), the leading DNN methods suffer from a huge performance drop. Inspired by the literature on generalized sampling, in this work we propose a method for improving the performance of DNNs that have been trained with a fixed kernel on observations acquired by other kernels. For a known kernel, we design a closed-form correction filter that modifies the low-resolution image to match one which is obtained by another kernel (e.g. bicubic), and thus improves the results of existing pre-trained DNNs. For an unknown kernel, we extend this idea and propose an algorithm for blind estimation of the required correction filter. We show that our approach outperforms other super-resolution methods, which are designed for general downscaling kernels.

We consider the problem of estimating the angles of arrival (AOAs) of multiple sources from a single snapshot obtained by a set of non-coherent sub-arrays, i.e., while the antenna elements in each sub-array are coherent, each sub-array observes a different unknown phase. Previous relevant works are based on eigendecomposition of the sample covariance, which requires a large number of snapshots, or on combining the sub-arrays using non-coherent processing methods. In this paper, we propose a technique to estimate the sub-arrays phase offsets for a given AOAs hypothesis, which facilitates approximate maximum likelihood estimation of the AOAs from a single snapshot. Numerical experiments show that the proposed approach clearly outperforms non-coherent processing, and even attains the Cramér-Rao lower bound in various scenarios.

Ill-posed linear inverse problems appear in many image processing applications, such as deblurring, superresolution and compressed sensing. Many restoration strategies involve minimizing a cost function, which is composed of fidelity and prior terms, balanced by a regularization parameter. While a vast amount of research has been focused on different prior models, the fidelity term is almost always chosen to be the least squares (LS) objective, that encourages fitting the linearly transformed optimization variable to the observations. In this paper, we examine a different fidelity term, which has been implicitly used by the recently proposed iterative denoising and backward projections (IDBP) framework. This term encourages agreement between the projection of the optimization variable onto the row space of the linear operator and the pseudoinverse of the linear operator ("back-projection") applied on the observations. We analytically examine the difference between the two fidelity terms for Tikhonov regularization and identify cases (such as a badly conditioned linear operator) where the new term has an advantage over the standard LS one. Moreover, we demonstrate empirically that the behavior of the two induced cost functions for sophisticated convex and non-convex priors, such as total-variation, BM3D, and deep generative models, correlates with the obtained theoretical analysis.

The problem of estimating the number of sources and their angles of arrival from a single antenna array observation has been an active area of research in the signal processing community for the last few decades. When the number of sources is large, the maximum likelihood estimator is intractable due to its very high complexity, and therefore alternative signal processing methods have been developed with some performance loss. In this paper, we apply a deep neural network (DNN) approach to the problem and analyze its advantages with respect to signal processing algorithms. We show that an appropriate designed network can attain the maximum likelihood performance with feasible complexity and outperform other feasible signal processing estimation methods over various signal to noise ratios and array response inaccuracies.

While deep neural networks exhibit state-of-the-art results in the task of image super-resolution (SR) with a fixed known acquisition process (e.g., a bicubic downscaling kernel), they experience a huge performance loss when the real observation model mismatches the one used in training. Recently, two different techniques suggested to mitigate this deficiency, i.e., enjoy the advantages of deep learning without being restricted by the training phase. The first one follows the plug-and-play (P&P) approach that solves general inverse problems (e.g., SR) by using Gaussian denoisers for handling the prior term in model-based optimization schemes. The second builds on internal recurrence of information inside a single image, and trains a super-resolver network at test time on examples synthesized from the low-resolution image. Our letter incorporates these two independent strategies, enjoying the impressive generalization capabilities of deep learning, captured by the first, and further improving it through internal learning at test time. First, we apply a recent P&P strategy to SR. Then, we show how it may become image-adaptive in test time. This technique outperforms the above two strategies on popular datasets and gives better results than other state-of-the-art methods in practical cases where the observation model is inexact or unknown in advance.

Inverse problems appear in many applications, such as image deblurring and inpainting. The common approach to address them is to design a specific algorithm for each problem. The Plug-and-Play (P&P) framework, which has been recently introduced, allows solving general inverse problems by leveraging the impressive capabilities of existing denoising algorithms. While this fresh strategy has found many applications, a burdensome parameter tuning is often required in order to obtain high-quality results. In this paper, we propose an alternative method for solving inverse problems using off-the-shelf denoisers, which requires less parameter tuning. First, we transform a typical cost function, composed of fidelity and prior terms, into a closely related, novel optimization problem. Then, we propose an efficient minimization scheme with a P&P property, i.e., the prior term is handled solely by a denoising operation. Finally, we present an automatic tuning mechanism to set the method's parameters. We provide a theoretical analysis of the method and empirically demonstrate its competitiveness with task-specific techniques and the P&P approach for image inpainting and deblurring.

In blind deblurring, the goal is to recover a latent sharp image from its blurred version when the blur kernel is unknown. In this case, natural image priors often lead to intractable algorithms or failures if used with maximum a posteriori (MAP) estimation. Therefore, the ruling approach is to start with estimating only the kernel, and then use it to recover the latent image via non-blind deblurring. While many blind deblurring works focus on the kernel estimation, we consider the second phase, where we build on the recently proposed Iterative Denoising and Backward Projections (IDBP) strategy. The proposed method uses an automatic parameters tuning mechanism, which can tune the parameters differently for each kernel and image, contrary to other deblurring algorithms that are restricted to a uniform tuning in the blind-deblurring setting. We demonstrate the advantages of our method over widely used deblurring algorithms.

The most common methods for localization of radio frequency transmitters are based on two processing steps. In the first step, parameters such as angle of arrival or time of arrival are estimated at each base station independently. In the second step, the estimated parameters are used to determine the location of the transmitters. The direct position determination approach advocates using the observations from all the base stations together in order to estimate the locations in a single step. This single-step method is known to outperform two-step methods when the signal-to-noise ratio is low. In this paper, we propose a direct-position-determination-based method for localization of multiple emitters that transmit unknown signals. The method does not require knowledge of the number of emitters. It is based on minimum-variance-distortionless-response considerations to achieve a high resolution estimator that requires only a two-dimensional search for planar geometry, and a three-dimensional search for the general case.