arXiv subjects

Ulugbek S. Kamilov

Publications and source records attributed to Ulugbek S. Kamilov.

At least 37 records · Page 2Linked to original sources

arXiv2025

Unsupervised Detection of Distribution Shift in Inverse Problems using Diffusion Models

Diffusion models are widely used as priors in imaging inverse problems. However, their performance often degrades under distribution shifts between the training and test-time images. Existing methods for identifying and quantifying distribution shifts typically require access to clean test images, which are almost never available while solving inverse problems (at test time). We propose a fully unsupervised metric for estimating distribution shifts using only indirect (corrupted) measurements and score functions from diffusion models trained on different datasets. We theoretically show that this metric estimates the KL divergence between the training and test image distributions. Empirically, we show that our score-based metric, using only corrupted measurements, closely approximates the KL divergence computed from clean images. Motivated by this result, we show that aligning the out-of-distribution score with the in-distribution score -- using only corrupted measurements -- reduces the KL divergence and leads to improved reconstruction quality across multiple inverse problems.

cs.CV↗

arXiv2025

Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problems

Diffusion models are extensively used for modeling image priors for inverse problems. We introduce \emph{Diff-Unfolding}, a principled framework for learning posterior score functions of \emph{conditional diffusion models} by explicitly incorporating the physical measurement operator into a modular network architecture. Diff-Unfolding formulates posterior score learning as the training of an unrolled optimization scheme, where the measurement model is decoupled from the learned image prior. This design allows our method to generalize across inverse problems at inference time by simply replacing the forward operator without retraining. We theoretically justify our unrolling approach by showing that the posterior score can be derived from a composite model-based optimization formulation. Extensive experiments on image restoration and accelerated MRI show that Diff-Unfolding achieves state-of-the-art performance, improving PSNR by up to 2 dB and reducing LPIPS by $22.7\%$, while being both compact (47M parameters) and efficient (0.72 seconds per $256 \times 256$ image). An optimized C++/LibTorch implementation further reduces inference time to 0.63 seconds, underscoring the practicality of our approach.

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arXiv2025

Measurement Score-Based Diffusion Model

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce the Measurement Score-based diffusion Model (MSM), a novel framework that learns partial measurement scores using only noisy and subsampled measurements. MSM models the distribution of full measurements as an expectation over partial scores induced by randomized subsampling. To make the MSM representation computationally efficient, we also develop a stochastic sampling algorithm that generates full images by using a randomly selected subset of partial scores at each step. We additionally propose a new posterior sampling method for solving inverse problems that reconstructs images using these partial scores. We provide a theoretical analysis that bounds the Kullback-Leibler divergence between the distributions induced by full and stochastic sampling, establishing the accuracy of the proposed algorithm. We demonstrate the effectiveness of MSM on natural images and multi-coil MRI, showing that it can generate high-quality images and solve inverse problems -- all without access to clean training data. Code is available at https://github.com/wustl-cig/MSM.

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arXiv2025

Multimodal Diffusion Bridge with Attention-Based SAR Fusion for Satellite Image Cloud Removal

Deep learning has achieved some success in addressing the challenge of cloud removal in optical satellite images, by fusing with synthetic aperture radar (SAR) images. Recently, diffusion models have emerged as powerful tools for cloud removal, delivering higher-quality estimation by sampling from cloud-free distributions, compared to earlier methods. However, diffusion models initiate sampling from pure Gaussian noise, which complicates the sampling trajectory and results in suboptimal performance. Also, current methods fall short in effectively fusing SAR and optical data. To address these limitations, we propose Diffusion Bridges for Cloud Removal, DB-CR, which directly bridges between the cloudy and cloud-free image distributions. In addition, we propose a novel multimodal diffusion bridge architecture with a two-branch backbone for multimodal image restoration, incorporating an efficient backbone and dedicated cross-modality fusion blocks to effectively extract and fuse features from synthetic aperture radar (SAR) and optical images. By formulating cloud removal as a diffusion-bridge problem and leveraging this tailored architecture, DB-CR achieves high-fidelity results while being computationally efficient. We evaluated DB-CR on the SEN12MS-CR cloud-removal dataset, demonstrating that it achieves state-of-the-art results.

cs.CV↗

arXiv2025

Efficient Model-Based Deep Learning via Network Pruning and Fine-Tuning

Model-based deep learning (MBDL) is a powerful methodology for designing deep models to solve imaging inverse problems. MBDL networks can be seen as iterative algorithms that estimate the desired image using a physical measurement model and a learned image prior specified using a convolutional neural net (CNNs). The iterative nature of MBDL networks increases the test-time computational complexity, which limits their applicability in certain large-scale applications. Here we make two contributions to address this issue: First, we show how structured pruning can be adopted to reduce the number of parameters in MBDL networks. Second, we present three methods to fine-tune the pruned MBDL networks to mitigate potential performance loss. Each fine-tuning strategy has a unique benefit that depends on the presence of a pre-trained model and a high-quality ground truth. We show that our pruning and fine-tuning approach can accelerate image reconstruction using popular deep equilibrium learning (DEQ) and deep unfolding (DU) methods by 50% and 32%, respectively, with nearly no performance loss. This work thus offers a step forward for solving inverse problems by showing the potential of pruning to improve the scalability of MBDL. Code is available at https://github.com/wustl-cig/MBDL_Pruning .

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arXiv2025

RELD: Regularization by Latent Diffusion Models for Image Restoration

In recent years, Diffusion Models have become the new state-of-the-art in deep generative modeling, ending the long-time dominance of Generative Adversarial Networks. Inspired by the Regularization by Denoising principle, we introduce an approach that integrates a Latent Diffusion Model, trained for the denoising task, into a variational framework using Half-Quadratic Splitting, exploiting its regularization properties. This approach, under appropriate conditions that can be easily met in various imaging applications, allows for reduced computational cost while achieving high-quality results. The proposed strategy, called Regularization by Latent Denoising (RELD), is then tested on a dataset of natural images, for image denoising, deblurring, and super-resolution tasks. The numerical experiments show that RELD is competitive with other state-of-the-art methods, particularly achieving remarkable results when evaluated using perceptual quality metrics.

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arXiv2025

Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models

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.

stat.ML↗

arXiv2025

CoRRECT: A Deep Unfolding Framework for Motion-Corrected Quantitative R2* Mapping

Quantitative MRI (qMRI) refers to a class of MRI methods for quantifying the spatial distribution of biological tissue parameters. Traditional qMRI methods usually deal separately with artifacts arising from accelerated data acquisition, involuntary physical motion, and magnetic-field inhomogeneities, leading to suboptimal end-to-end performance. This paper presents CoRRECT, a unified deep unfolding (DU) framework for qMRI consisting of a model-based end-to-end neural network, a method for motion-artifact reduction, and a self-supervised learning scheme. The network is trained to produce R2* maps whose k-space data matches the real data by also accounting for motion and field inhomogeneities. When deployed, CoRRECT only uses the k-space data without any pre-computed parameters for motion or inhomogeneity correction. Our results on experimentally collected multi-Gradient-Recalled Echo (mGRE) MRI data show that CoRRECT recovers motion and inhomogeneity artifact-free R2* maps in highly accelerated acquisition settings. This work opens the door to DU methods that can integrate physical measurement models, biophysical signal models, and learned prior models for high-quality qMRI.

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arXiv2025

A Self-supervised Diffusion Bridge for MRI Reconstruction

Diffusion bridges (DBs) are a class of diffusion models that enable faster sampling by interpolating between two paired image distributions. Training traditional DBs for image reconstruction requires high-quality reference images, which limits their applicability to settings where such references are unavailable. We propose SelfDB as a novel self-supervised method for training DBs directly on available noisy measurements without any high-quality reference images. SelfDB formulates the diffusion process by further sub-sampling the available measurements two additional times and training a neural network to reverse the corresponding degradation process by using the available measurements as the training targets. We validate SelfDB on compressed sensing MRI, showing its superior performance compared to the denoising diffusion models.

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arXiv2024

A Generalizable 3D Diffusion Framework for Low-Dose and Few-View Cardiac SPECT

Myocardial perfusion imaging using SPECT is widely utilized to diagnose coronary artery diseases, but image quality can be negatively affected in low-dose and few-view acquisition settings. Although various deep learning methods have been introduced to improve image quality from low-dose or few-view SPECT data, previous approaches often fail to generalize across different acquisition settings, limiting their applicability in reality. This work introduced DiffSPECT-3D, a diffusion framework for 3D cardiac SPECT imaging that effectively adapts to different acquisition settings without requiring further network re-training or fine-tuning. Using both image and projection data, a consistency strategy is proposed to ensure that diffusion sampling at each step aligns with the low-dose/few-view projection measurements, the image data, and the scanner geometry, thus enabling generalization to different low-dose/few-view settings. Incorporating anatomical spatial information from CT and total variation constraint, we proposed a 2.5D conditional strategy to allow the DiffSPECT-3D to observe 3D contextual information from the entire image volume, addressing the 3D memory issues in diffusion model. We extensively evaluated the proposed method on 1,325 clinical 99mTc tetrofosmin stress/rest studies from 795 patients. Each study was reconstructed into 5 different low-count and 5 different few-view levels for model evaluations, ranging from 1% to 50% and from 1 view to 9 view, respectively. Validated against cardiac catheterization results and diagnostic comments from nuclear cardiologists, the presented results show the potential to achieve low-dose and few-view SPECT imaging without compromising clinical performance. Additionally, DiffSPECT-3D could be directly applied to full-dose SPECT images to further improve image quality, especially in a low-dose stress-first cardiac SPECT imaging protocol.

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arXiv2024

Plug-and-Play Priors as a Score-Based Method

Plug-and-play (PnP) methods are extensively used for solving imaging inverse problems by integrating physical measurement models with pre-trained deep denoisers as priors. Score-based diffusion models (SBMs) have recently emerged as a powerful framework for image generation by training deep denoisers to represent the score of the image prior. While both PnP and SBMs use deep denoisers, the score-based nature of PnP is unexplored in the literature due to its distinct origins rooted in proximal optimization. This letter introduces a novel view of PnP as a score-based method, a perspective that enables the re-use of powerful SBMs within classical PnP algorithms without retraining. We present a set of mathematical relationships for adapting popular SBMs as priors within PnP. We show that this approach enables a direct comparison between PnP and SBM-based reconstruction methods using the same neural network as the prior. Code is available at https://github.com/wustl-cig/score_pnp.

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arXiv2024

ADOBI: Adaptive Diffusion Bridge For Blind Inverse Problems with Application to MRI Reconstruction

Diffusion bridges (DB) have emerged as a promising alternative to diffusion models for imaging inverse problems, achieving faster sampling by directly bridging low- and high-quality image distributions. While incorporating measurement consistency has been shown to improve performance, existing DB methods fail to maintain this consistency in blind inverse problems, where the forward model is unknown. To address this limitation, we introduce ADOBI (Adaptive Diffusion Bridge for Inverse Problems), a novel framework that adaptively calibrates the unknown forward model to enforce measurement consistency throughout sampling iterations. Our adaptation strategy allows ADOBI to achieve high-quality parallel magnetic resonance imaging (PMRI) reconstruction in only 5-10 steps. Our numerical results show that ADOBI consistently delivers state-of-the-art performance, and further advances the Pareto frontier for the perception-distortion trade-off.

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arXiv2024

Stochastic Deep Restoration Priors for Imaging Inverse Problems

Deep neural networks trained as image denoisers are widely used as priors for solving imaging inverse problems. While Gaussian denoising is thought sufficient for learning image priors, we show that priors from deep models pre-trained as more general restoration operators can perform better. We introduce Stochastic deep Restoration Priors (ShaRP), a novel method that leverages an ensemble of such restoration models to regularize inverse problems. ShaRP improves upon methods using Gaussian denoiser priors by better handling structured artifacts and enabling self-supervised training even without fully sampled data. We prove ShaRP minimizes an objective function involving a regularizer derived from the score functions of minimum mean square error (MMSE) restoration operators, and theoretically analyze its convergence. Empirically, ShaRP achieves state-of-the-art performance on tasks such as magnetic resonance imaging reconstruction and single-image super-resolution, surpassing both denoiser-and diffusion-model-based methods without requiring retraining.

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arXiv2024

SPICER: Self-Supervised Learning for MRI with Automatic Coil Sensitivity Estimation and Reconstruction

Deep model-based architectures (DMBAs) integrating physical measurement models and learned image regularizers are widely used in parallel magnetic resonance imaging (PMRI). Traditional DMBAs for PMRI rely on pre-estimated coil sensitivity maps (CSMs) as a component of the measurement model. However, estimation of accurate CSMs is a challenging problem when measurements are highly undersampled. Additionally, traditional training of DMBAs requires high-quality groundtruth images, limiting their use in applications where groundtruth is difficult to obtain. This paper addresses these issues by presenting SPICE as a new method that integrates self-supervised learning and automatic coil sensitivity estimation. Instead of using pre-estimated CSMs, SPICE simultaneously reconstructs accurate MR images and estimates high-quality CSMs. SPICE also enables learning from undersampled noisy measurements without any groundtruth. We validate SPICE on experimentally collected data, showing that it can achieve state-of-the-art performance in highly accelerated data acquisition settings (up to 10x).

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arXiv2024

TVCondNet: A Conditional Denoising Neural Network for NMR Spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a widely-used technique in the fields of bio-medicine, chemistry, and biology for the analysis of chemicals and proteins. The signals from NMR spectroscopy often have low signal-to-noise ratio (SNR) due to acquisition noise, which poses significant challenges for subsequent analysis. Recent work has explored the potential of deep learning (DL) for NMR denoising, showing significant performance gains over traditional methods such as total variation (TV) denoising. This paper shows that the performance of DL denoising for NMR can be further improved by combining data-driven training with traditional TV denoising. The proposed TVCondNet method outperforms both traditional TV and DL methods by including the TV solution as a condition during DL training. Our validation on experimentally collected NMR data shows the superior denoising performance and faster inference speed of TVCondNet compared to existing methods.

eess.SP↗

arXiv2024

DiffGEPCI: 3D MRI Synthesis from mGRE Signals using 2.5D Diffusion Model

We introduce a new framework called DiffGEPCI for cross-modality generation in magnetic resonance imaging (MRI) using a 2.5D conditional diffusion model. DiffGEPCI can synthesize high-quality Fluid Attenuated Inversion Recovery (FLAIR) and Magnetization Prepared-Rapid Gradient Echo (MPRAGE) images, without acquiring corresponding measurements, by leveraging multi-Gradient-Recalled Echo (mGRE) MRI signals as conditional inputs. DiffGEPCI operates in a two-step fashion: it initially estimates a 3D volume slice-by-slice using the axial plane and subsequently applies a refinement algorithm (referred to as 2.5D) to enhance the quality of the coronal and sagittal planes. Experimental validation on real mGRE data shows that DiffGEPCI achieves excellent performance, surpassing generative adversarial networks (GANs) and traditional diffusion models.

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arXiv2024

Pseudo-MRI-Guided PET Image Reconstruction Method Based on a Diffusion Probabilistic Model

Anatomically guided PET reconstruction using MRI information has been shown to have the potential to improve PET image quality. However, these improvements are limited to PET scans with paired MRI information. In this work we employed a diffusion probabilistic model (DPM) to infer T1-weighted-MRI (deep-MRI) images from FDG-PET brain images. We then use the DPM-generated T1w-MRI to guide the PET reconstruction. The model was trained with brain FDG scans, and tested in datasets containing multiple levels of counts. Deep-MRI images appeared somewhat degraded than the acquired MRI images. Regarding PET image quality, volume of interest analysis in different brain regions showed that both PET reconstructed images using the acquired and the deep-MRI images improved image quality compared to OSEM. Same conclusions were found analysing the decimated datasets. A subjective evaluation performed by two physicians confirmed that OSEM scored consistently worse than the MRI-guided PET images and no significant differences were observed between the MRI-guided PET images. This proof of concept shows that it is possible to infer DPM-based MRI imagery to guide the PET reconstruction, enabling the possibility of changing reconstruction parameters such as the strength of the prior on anatomically guided PET reconstruction in the absence of MRI.

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arXiv2024

A Plug-and-Play Image Registration Network

Deformable image registration (DIR) is an active research topic in biomedical imaging. There is a growing interest in developing DIR methods based on deep learning (DL). A traditional DL approach to DIR is based on training a convolutional neural network (CNN) to estimate the registration field between two input images. While conceptually simple, this approach comes with a limitation that it exclusively relies on a pre-trained CNN without explicitly enforcing fidelity between the registered image and the reference. We present plug-and-play image registration network (PIRATE) as a new DIR method that addresses this issue by integrating an explicit data-fidelity penalty and a CNN prior. PIRATE pre-trains a CNN denoiser on the registration field and "plugs" it into an iterative method as a regularizer. We additionally present PIRATE+ that fine-tunes the CNN prior in PIRATE using deep equilibrium models (DEQ). PIRATE+ interprets the fixed-point iteration of PIRATE as a network with effectively infinite layers and then trains the resulting network end-to-end, enabling it to learn more task-specific information and boosting its performance. Our numerical results on OASIS and CANDI datasets show that our methods achieve state-of-the-art performance on DIR.

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