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Register a new userJoint Reconstruction and Calibration using Regularization by Denoising
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Regularization by denoising (RED) is a broadly applicable framework for solving inverse problems by using priors specified as denoisers. While RED has been shown to provide state-of-the-art performance in a number of applications, existing RED algorithms require exact knowledge of the measurement operator characterizing the imaging system, limiting their applicability in problems where the measurement operator has parametric uncertainties. We propose a new method, called Calibrated RED (Cal-RED), that enables joint calibration of the measurement operator along with reconstruction of the unknown image. Cal-RED extends the traditional RED methodology to imaging problems that require the calibration of the measurement operator. We validate Cal-RED on the problem of image reconstruction in computerized tomography (CT) under perturbed projection angles. Our results corroborate the effectiveness of Cal-RED for joint calibration and reconstruction using pre-trained deep denoisers as image priors.
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Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this limitation by introducing a novel online RED (On-RED) algorithm, which processes a small subset of the data at a time. We establish the theoretical convergence of On-RED in convex settings and empirically discuss its effectiveness in non-convex ones by illustrating its applicability to phase retrieval. Our results suggest that On-RED is an effective alternative to the traditional RED algorithms when dealing with large datasets.
Inverse problems in image processing are typically cast as optimization tasks, consisting of data-fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to bridge between RED and PnP, enriching the understanding of both frameworks. Towards that end, we reformulate RED as a convex optimization problem utilizing a projection (RED-PRO) onto the fixed-point set of demicontractive denoisers. We offer a simple iterative solution to this problem, by which we show that PnP proximal gradient method is a special case of RED-PRO, while providing guarantees for the convergence of both frameworks to globally optimal solutions. In addition, we present relaxations of RED-PRO that allow for handling denoisers with limited fixed-point sets. Finally, we demonstrate RED-PRO for the tasks of image deblurring and super-resolution, showing improved results with respect to the original RED framework.
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.
Most consumer-grade digital cameras can only capture a limited range of luminance in real-world scenes due to sensor constraints. Besides, noise and quantization errors are often introduced in the imaging process. In order to obtain high dynamic range (HDR) images with excellent visual quality, the most common solution is to combine multiple images with different exposures. However, it is not always feasible to obtain multiple images of the same scene and most HDR reconstruction methods ignore the noise and quantization loss. In this work, we propose a novel learning-based approach using a spatially dynamic encoder-decoder network, HDRUNet, to learn an end-to-end mapping for single image HDR reconstruction with denoising and dequantization. The network consists of a UNet-style base network to make full use of the hierarchical multi-scale information, a condition network to perform pattern-specific modulation and a weighting network for selectively retaining information. Moreover, we propose a Tanh_L1 loss function to balance the impact of over-exposed values and well-exposed values on the network learning. Our method achieves the state-of-the-art performance in quantitative comparisons and visual quality. The proposed HDRUNet model won the second place in the single frame track of NITRE2021 High Dynamic Range Challenge.
Reconstructing under-sampled k-space measurements in Compressed Sensing MRI (CS-MRI) is classically solved with regularized least-squares. Recently, deep learning has been used to amortize this optimization by training reconstruction networks on a dataset of under-sampled measurements. Here, a crucial design choice is the regularization function(s) and corresponding weight(s). In this paper, we explore a novel strategy of using a hypernetwork to generate the parameters of a separate reconstruction network as a function of the regularization weight(s), resulting in a regularization-agnostic reconstruction model. At test time, for a given under-sampled image, our model can rapidly compute reconstructions with different amounts of regularization. We analyze the variability of these reconstructions, especially in situations when the overall quality is similar. Finally, we propose and empirically demonstrate an efficient and data-driven way of maximizing reconstruction performance given limited hypernetwork capacity. Our code is publicly available at https://github.com/alanqrwang/RegAgnosticCSMRI.
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