arXiv subjects

Ulugbek S. Kamilov

Publications and source records attributed to Ulugbek S. Kamilov.

At least 91 records · Page 5Linked to original sources

arXiv2020

Provable Convergence of Plug-and-Play Priors with MMSE denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

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arXiv2020

Deep learning using a biophysical model for Robust and Accelerated Reconstruction (RoAR) of quantitative and artifact-free R2* images

Purpose: To introduce a novel deep learning method for Robust and Accelerated Reconstruction (RoAR) of quantitative and B0-inhomogeneity-corrected R2* maps from multi-gradient recalled echo (mGRE) MRI data. Methods: RoAR trains a convolutional neural network (CNN) to generate quantitative R2* maps free from field inhomogeneity artifacts by adopting a self-supervised learning strategy given (a) mGRE magnitude images, (b) the biophysical model describing mGRE signal decay, and (c) preliminary-evaluated F-function accounting for contribution of macroscopic B0 field inhomogeneities. Importantly, no ground-truth R2* images are required and F-function is only needed during RoAR training but not application. Results: We show that RoAR preserves all features of R2* maps while offering significant improvements over existing methods in computation speed (seconds vs. hours) and reduced sensitivity to noise. Even for data with SNR=5 RoAR produced R2* maps with accuracy of 22% while voxel-wise analysis accuracy was 47%. For SNR=10 the RoAR accuracy increased to 17% vs. 24% for direct voxel-wise analysis. Conclusion: RoAR is trained to recognize the macroscopic magnetic field inhomogeneities directly from the input magnitude-only mGRE data and eliminate their effect on R2* measurements. RoAR training is based on the biophysical model and does not require ground-truth R2* maps. Since RoAR utilizes signal information not just from individual voxels but also accounts for spatial patterns of the signals in the images, it reduces the sensitivity of R2* maps to the noise in the data. These features plus high computational speed provide significant benefits for the potential usage of RoAR in clinical settings.

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arXiv2020

Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling

Plug-and-play priors (PnP) is an image reconstruction framework that uses an image denoiser as an imaging prior. Unlike traditional regularized inversion, PnP does not require the prior to be expressible in the form of a regularization function. This flexibility enables PnP algorithms to exploit the most effective image denoisers, leading to their state-of-the-art performance in various imaging tasks. In this paper, we propose a new denoiser scaling technique to explicitly control the amount of PnP regularization. Traditionally, the performance of PnP algorithms is controlled via intrinsic parameters of the denoiser related to the noise variance. However, many powerful denoisers, such as the ones based on convolutional neural networks (CNNs), do not have tunable parameters that would allow controlling their influence within PnP. To address this issue, we introduce a scaling parameter that adjusts the magnitude of the denoiser input and output. We theoretical justify the denoiser scaling from the perspectives of proximal optimization, statistical estimation, and consensus equilibrium. Finally, we provide numerical experiments demonstrating the ability of denoiser scaling to systematically improve the performance of PnP for denoising CNN priors that do not have explicitly tunable parameters.

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arXiv2019

Proximal Newton Methods for X-Ray Imaging with Non-Smooth Regularization

Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a smooth data-fidelity term and total variation (TV) regularization arising from image reconstruction applications. Specifically, we consider a nonlinear Poisson-modeled single-energy X-ray computed tomography reconstruction problem with the data-fidelity term given by the I-divergence. The PN algorithm is compared to state-of-the-art first-order proximal algorithms, such as the well-established fast iterative shrinkage and thresholding algorithm (FISTA), both in terms of the number of iterations and time to solutions. We discuss the key factors that influence the performance of PN, including the strength of regularization, the stopping criterion for both sub-problem and main-problem, and the use of exact or approximated Hessian operators.

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arXiv2019

Infusing Learned Priors into Model-Based Multispectral Imaging

We introduce a new algorithm for regularized reconstruction of multispectral (MS) images from noisy linear measurements. Unlike traditional approaches, the proposed algorithm regularizes the recovery problem by using a prior specified \emph{only} through a learned denoising function. More specifically, we propose a new accelerated gradient method (AGM) variant of regularization by denoising (RED) for model-based MS image reconstruction. The key ingredient of our approach is the three-dimensional (3D) deep neural net (DNN) denoiser that can fully leverage spationspectral correlations within MS images. Our results suggest the generalizability of our MS-RED algorithm, where a single trained DNN can be used to solve several different MS imaging problems.

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arXiv2019

Block Coordinate Regularization by Denoising

We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance of estimators under such priors in a range of imaging tasks. In this work, we develop a new block coordinate RED algorithm that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables. We theoretically analyze the convergence of the algorithm and discuss its relationship to the traditional proximal optimization. Our analysis complements and extends recent theoretical results for RED-based estimation methods. We numerically validate our method using several denoiser priors, including those based on convolutional neural network (CNN) denoisers.

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arXiv2019

Online Regularization by Denoising with Applications to Phase Retrieval

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.

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arXiv2019

A New Recurrent Plug-and-Play Prior Based on the Multiple Self-Similarity Network

Recent work has shown the effectiveness of the plug-and-play priors (PnP) framework for regularized image reconstruction. However, the performance of PnP depends on the quality of the denoisers used as priors. In this letter, we design a novel PnP denoising prior, called multiple self-similarity net (MSSN), based on the recurrent neural network (RNN) with self-similarity matching using multi-head attention mechanism. Unlike traditional neural net denoisers, MSSN exploits different types of relationships among non-local and repeating features to remove the noise in the input image. We numerically evaluate the performance of MSSN as a module within PnP for solving magnetic resonance (MR) image reconstruction. Experimental results show the stable convergence and excellent performance of MSSN for reconstructing images from highly compressive Fourier measurements.

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arXiv2019

Holographic particle localization under multiple scattering

We introduce a novel framework that incorporates multiple scattering for large-scale 3D particle-localization using single-shot in-line holography. Traditional holographic techniques rely on single-scattering models which become inaccurate under high particle-density. We demonstrate that by exploiting multiple-scattering, localization is significantly improved. Both forward and back-scattering are computed by our method under a tractable recursive framework, in which each recursion estimates the next higher-order field within the volume. The inverse scattering is presented as a nonlinear optimization that promotes sparsity, and can be implemented efficiently. We experimentally reconstruct 100 million object voxels from a single 1-megapixel hologram. Our work promises utilization of multiple scattering for versatile large-scale applications.

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arXiv2018

Stability of Scattering Decoder For Nonlinear Diffractive Imaging

The problem of image reconstruction under multiple light scattering is usually formulated as a regularized non-convex optimization. A deep learning architecture, Scattering Decoder (ScaDec), was recently proposed to solve this problem in a purely data-driven fashion. The proposed method was shown to substantially outperform optimization-based baselines and achieve state-of-the-art results. In this paper, we thoroughly test the robustness of ScaDec to different permittivity contrasts, number of transmissions, and input signal-to-noise ratios. The results on high-fidelity simulated datasets show that the performance of ScaDec is stable in different settings.

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arXiv2018

Plug-In Stochastic Gradient Method

Plug-and-play priors (PnP) is a popular framework for regularized signal reconstruction by using advanced denoisers within an iterative algorithm. In this paper, we discuss our recent online variant of PnP that uses only a subset of measurements at every iteration, which makes it scalable to very large datasets. We additionally present novel convergence results for both batch and online PnP algorithms.

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arXiv2018

Regularized Fourier Ptychography using an Online Plug-and-Play Algorithm

The plug-and-play priors (PnP) framework has been recently shown to achieve state-of-the-art results in regularized image reconstruction by leveraging a sophisticated denoiser within an iterative algorithm. In this paper, we propose a new online PnP algorithm for Fourier ptychographic microscopy (FPM) based on the fast iterative shrinkage/threshold algorithm (FISTA). Specifically, the proposed algorithm uses only a subset of measurements, which makes it scalable to a large set of measurements. We validate the algorithm by showing that it can lead to significant performance gains on both simulated and experimental data.

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arXiv2018

Image Restoration using Total Variation Regularized Deep Image Prior

In the past decade, sparsity-driven regularization has led to significant improvements in image reconstruction. Traditional regularizers, such as total variation (TV), rely on analytical models of sparsity. However, increasingly the field is moving towards trainable models, inspired from deep learning. Deep image prior (DIP) is a recent regularization framework that uses a convolutional neural network (CNN) architecture without data-driven training. This paper extends the DIP framework by combining it with the traditional TV regularization. We show that the inclusion of TV leads to considerable performance gains when tested on several traditional restoration tasks such as image denoising and deblurring.

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arXiv2018

signProx: One-Bit Proximal Algorithm for Nonconvex Stochastic Optimization

Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the gradients between different computation nodes. To reduce this communication bottleneck, recent work has considered a one-bit variant of SGD, where only the sign of each gradient element is used in optimization. In this paper, we extend this idea by proposing a stochastic variant of the proximal-gradient method that also uses one-bit per update element. We prove the theoretical convergence of the method for non-convex optimization under a set of explicit assumptions. Our results indicate that the compressed method can match the convergence rate of the uncompressed one, making the proposed method potentially appealing for distributed processing of large datasets.

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arXiv2018

An Online Plug-and-Play Algorithm for Regularized Image Reconstruction

Plug-and-play priors (PnP) is a powerful framework for regularizing imaging inverse problems by using advanced denoisers within an iterative algorithm. Recent experimental evidence suggests that PnP algorithms achieve state-of-the-art performance in a range of imaging applications. In this paper, we introduce a new online PnP algorithm based on the iterative shrinkage/thresholding algorithm (ISTA). The proposed algorithm uses only a subset of measurements at every iteration, which makes it scalable to very large datasets. We present a new theoretical convergence analysis, for both batch and online variants of PnP-ISTA, for denoisers that do not necessarily correspond to proximal operators. We also present simulations illustrating the applicability of the algorithm to image reconstruction in diffraction tomography. The results in this paper have the potential to expand the applicability of the PnP framework to very large and redundant datasets.

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arXiv2018

Sparse Blind Deconvolution for Distributed Radar Autofocus Imaging

A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus. Common techniques that attempt to resolve the antenna ambiguity generally assume an unknown gain and phase error afflicting the radar measurements. However, ensuring identifiability and tractability of the unknown error imposes strict restrictions on the allowable antenna perturbations. Furthermore, these techniques are often not applicable in near-field imaging, where mapping the position ambiguity to phase errors breaks down. In this paper, we propose an alternate formulation where the position error of each antenna is mapped to a spatial shift operator in the image-domain. Thus, the radar autofocus problem becomes a multichannel blind deconvolution problem, in which the radar measurements correspond to observations of a static radar image that is convolved with the spatial shift kernel associated with each antenna. To solve the reformulated problem, we also develop a block coordinate descent framework that leverages the sparsity and piece-wise smoothness of the radar scene, as well as the one-sparse property of the two dimensional shift kernels. We evaluate the performance of our approach using both simulated and experimental radar measurements, and demonstrate its superior performance compared to state-of-the-art methods.

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arXiv2018

Efficient and accurate inversion of multiple scattering with deep learning

Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is used to account for multiple scattering and regularization is used to enforce prior constraints on the object. In this paper, we propose a powerful alternative to this optimization-based view of image reconstruction by designing and training a deep convolutional neural network that can invert multiple scattered measurements to produce a high-quality image of the refractive index. Our results on both simulated and experimental datasets show that the proposed approach is substantially faster and achieves higher imaging quality compared to the state-of-the-art methods based on optimization.

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arXiv2018

Learning-based Image Reconstruction via Parallel Proximal Algorithm

In the past decade, sparsity-driven regularization has led to advancement of image reconstruction algorithms. Traditionally, such regularizers rely on analytical models of sparsity (e.g. total variation (TV)). However, more recent methods are increasingly centered around data-driven arguments inspired by deep learning. In this letter, we propose to generalize TV regularization by replacing the l1-penalty with an alternative prior that is trainable. Specifically, our method learns the prior via extending the recently proposed fast parallel proximal algorithm (FPPA) to incorporate data-adaptive proximal operators. The proposed framework does not require additional inner iterations for evaluating the proximal mappings of the corresponding learned prior. Moreover, our formalism ensures that the training and reconstruction processes share the same algorithmic structure, making the end-to-end implementation intuitive. As an example, we demonstrate our algorithm on the problem of deconvolution in a fluorescence microscope.

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