arXiv subjects

Behzad Sharif

Publications and source records attributed to Behzad Sharif.

7 recordsLinked to original sources

arXiv2026

Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems

Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration. Although variance reduction techniques such as SGD with momentum, STORM, and PAGE have demonstrated improved convergence properties in non-convex optimization, their implications for sampling from non-log-concave distributions remain largely unexplored. In this work, we develop the first unified analysis of these estimators for sampling from non-log-concave distributions. We establish improved non-asymptotic convergence rates in $\varepsilon$-relative Fisher information and, under a Poincar\'e inequality assumption, in squared total variation distance, and further prove weak convergence to the target distribution. We extend our analysis to solving inverse problems with score-based generative priors. We empirically validate our theory and demonstrate that, under a fixed gradient computations per iteration, variance-reduction techniques consistently improve sample quality in two standard imaging applications.

cs.LG↗

arXiv2026

Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problems

Sampling from high-dimensional, non-log-concave distributions with unnormalized densities remains a fundamental challenge in machine learning, particularly in black-box settings where gradient information is inaccessible or computationally prohibitive. While Langevin dynamics provides a principled framework for sampling when gradients are accessible, its extension to the black-box settings suffers from high variance and lacks non-asymptotic convergence guarantees for non-log-concave sampling. To address these limitations, we propose a variance-reduced zeroth-order Langevin sampling method. Our method employs a gradient estimator that substantially reduces the variance of the classical batched zeroth-order estimator and eliminates the unfavorable dimensional dependence of the batch size required for accurate estimation, enabling practical and stable sampling. We establish the first non-asymptotic convergence guarantees for zeroth-order non-log-concave sampling in terms of $\varepsilon$-relative Fisher information, and, under a Poincar\'e inequality assumption, squared total variation distance. We further propose ZO-APMC, a posterior sampling algorithm for black-box inverse problems with pre-trained score-based generative priors, establishing the first non-asymptotic convergence guarantees for such methods. We validate our theory through synthetic experiments and demonstrate strong empirical performance on practical linear and nonlinear inverse problems.

cs.LG↗

arXiv2026

Phase-map synthesis from magnitude-only MR images using conditional score-based diffusion models with application in training of accelerated MRI reconstruction models

Accelerated magnetic resonance imaging (MRI) enabled by the training of deep learning (DL)-based image recon. models requires large and diverse raw k-space datasets. In most clinical MRI applications, due to storage and patient privacy concerns, raw k-space data is discarded and magnitude-only images are the only component saved. Consequently, a large portion of the DL-based MRI recon. literature has either relied on small training datasets or has used one of the few available open-source k-space datasets. At the same time, the growing number of anonymized magnitude-only image registries/databases motivates the development of techniques that can use them as training datasets for generalizable DL-based recon. models. Here we propose to address this challenge by employing a generative approach based on conditional score-based diffusion models (SBDMs): given a magnitude-only MR image, it synthesizes a phase map (in the image domain) that realistically corresponds to the magnitude-only image. We evaluate its generative capabilities in a downstream DL-based recon. task whereby a large k-space dataset is generated by combining the SBDM-synthesized phase-maps and the corresponding magnitude-only images, and this k-space dataset is then used to train a DL model for accelerated MRI recon. We compare the performance of the resulting DL model versus those trained according to (a) a naive approach that uses smooth phase, (b) a k-space training dataset generated using synthesized phase maps derived from a generative adversarial network, and (c) the ground truth k-space data. Our results suggest that the DL model trained from SBDM-synthesized k-space data outperforms the other approaches in terms of quantitative metrics as well as qualitatively observed recon. fidelity, i.e., whether the reconstructed images include erroneous or hallucinated features that could adversely impact diagnostic accuracy.

cs.CV↗

arXiv2026

RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolation

A celebrated method for Variational Inequalities (VIs) is Extragradient (EG), which can be viewed as a standard discrete-time integration scheme. With this view in mind, in this paper we show that EG may suffer from discretization bias when applied to non-linear vector fields, conservative or otherwise. To resolve this discretization shortcoming, we introduce RAndomized Mid-Point for debiAsed Gradient Extrapolation (RAMPAGE) and its variance-reduced counterpart, RAMPAGE+, which leverages antithetic sampling. In contrast with EG, both methods are unbiased. Furthermore, leveraging negative correlation, RAMPAGE+ acts as an unbiased, geometric path-integrator that completely removes internal first-order terms from the variance, provably improving upon RAMPAGE. We further demonstrate that both methods enjoy provable $\mathcal{O}(1/k)$ convergence guarantees for a range of problems including root finding under co-coercive, co-hypomonotone, and generalized Lipschitzness regimes. Furthermore, we introduce symmetrically scaled variants to extend our results to constrained VIs. Finally, we provide convergence guarantees of both methods for stochastic and deterministic smooth convex-concave games. Somewhat interestingly, despite being a randomized method, RAMPAGE+ attains purely deterministic bounds for a number of the studied settings.

cs.LG↗

arXiv2024

Improved Robustness for Deep Learning-based Segmentation of Multi-Center Myocardial Perfusion MRI Datasets Using Data Adaptive Uncertainty-guided Space-time Analysis

Background. Fully automatic analysis of myocardial perfusion MRI datasets enables rapid and objective reporting of stress/rest studies in patients with suspected ischemic heart disease. Developing deep learning techniques that can analyze multi-center datasets despite limited training data and variations in software and hardware is an ongoing challenge. Methods. Datasets from 3 medical centers acquired at 3T (n = 150 subjects) were included: an internal dataset (inD; n = 95) and two external datasets (exDs; n = 55) used for evaluating the robustness of the trained deep neural network (DNN) models against differences in pulse sequence (exD-1) and scanner vendor (exD-2). A subset of inD (n = 85) was used for training/validation of a pool of DNNs for segmentation, all using the same spatiotemporal U-Net architecture and hyperparameters but with different parameter initializations. We employed a space-time sliding-patch analysis approach that automatically yields a pixel-wise "uncertainty map" as a byproduct of the segmentation process. In our approach, a given test case is segmented by all members of the DNN pool and the resulting uncertainty maps are leveraged to automatically select the "best" one among the pool of solutions. Results. The proposed DAUGS analysis approach performed similarly to the established approach on the internal dataset (p = n.s.) whereas it significantly outperformed on the external datasets (p < 0.005 for exD-1 and exD-2). Moreover, the number of image series with "failed" segmentation was significantly lower for the proposed vs. the established approach (4.3% vs. 17.1%, p < 0.0005). Conclusions. The proposed DAUGS analysis approach has the potential to improve the robustness of deep learning methods for segmentation of multi-center stress perfusion datasets with variations in the choice of pulse sequence, site location or scanner vendor.

eess.IV↗

arXiv2023

Temporal Uncertainty Localization to Enable Human-in-the-loop Analysis of Dynamic Contrast-enhanced Cardiac MRI Datasets

Dynamic contrast-enhanced (DCE) cardiac magnetic resonance imaging (CMRI) is a widely used modality for diagnosing myocardial blood flow (perfusion) abnormalities. During a typical free-breathing DCE-CMRI scan, close to 300 time-resolved images of myocardial perfusion are acquired at various contrast "wash in/out" phases. Manual segmentation of myocardial contours in each time-frame of a DCE image series can be tedious and time-consuming, particularly when non-rigid motion correction has failed or is unavailable. While deep neural networks (DNNs) have shown promise for analyzing DCE-CMRI datasets, a "dynamic quality control" (dQC) technique for reliably detecting failed segmentations is lacking. Here we propose a new space-time uncertainty metric as a dQC tool for DNN-based segmentation of free-breathing DCE-CMRI datasets by validating the proposed metric on an external dataset and establishing a human-in-the-loop framework to improve the segmentation results. In the proposed approach, we referred the top 10% most uncertain segmentations as detected by our dQC tool to the human expert for refinement. This approach resulted in a significant increase in the Dice score (p<0.001) and a notable decrease in the number of images with failed segmentation (16.2% to 11.3%) whereas the alternative approach of randomly selecting the same number of segmentations for human referral did not achieve any significant improvement. Our results suggest that the proposed dQC framework has the potential to accurately identify poor-quality segmentations and may enable efficient DNN-based analysis of DCE-CMRI in a human-in-the-loop pipeline for clinical interpretation and reporting of dynamic CMRI datasets.

eess.IV↗

arXiv2011

Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems

We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with oversampling factors of at least two, we provide prescriptions for the shortest filter length of the synthesis bank that would guarantee PR almost surely. The prescribed length is as short or shorter than the analysis filters and has an approximate inverse relationship with the oversampling factor. Our results are in form of necessary and sufficient statements that hold generically, hence only fail for elaborately-designed nongeneric examples. We provide extensive numerical verification of the theoretical results and demonstrate that the gap between the derived filter length prescriptions and the true minimum is small. The results have potential applications in synthesis FB design problems, where the analysis bank is given, and for analysis of fundamental limitations in blind signals reconstruction from data collected by unknown subsampled multi-channel systems.

cs.IT↗