arXiv subjects

Alireza Entezari

Publications and source records attributed to Alireza Entezari.

8 recordsLinked to original sources

arXiv2025

Global Asymptotic Rates Under Randomization: Gauss-Seidel and Kaczmarz

Current performance bounds for randomized iterative methods are often considered tight under per-iteration analyses, yet they are notoriously loose in practice. We derive asymptotic performance bounds that narrow this theory-practice gap, leveraging a new technique for bounding the spectral radii of operators arising in randomized iterations and a connection we establish to Perron-Frobenius theory for noncommutative algebras. The asymptotic analysis also uncovers and quantifies the previously unexplained role of relaxation in improving performance, thereby resolving an open problem posed by Strohmer and Vershynin in 2007.

math.NA↗

arXiv2024

Residual Back Projection With Untrained Neural Networks

Background and Objective: The success of neural networks in a number of image processing tasks has motivated their application in image reconstruction problems in computed tomography (CT). While progress has been made in this area, the lack of stability and theoretical guarantees for accuracy, together with the scarcity of high-quality training data for specific imaging domains pose challenges for many CT applications. In this paper, we present a framework for iterative reconstruction (IR) in CT that leverages the hierarchical structure of neural networks, without the need for training. Our framework incorporates this structural information as a deep image prior (DIP), and uses a novel residual back projection (RBP) connection that forms the basis for our iterations. Methods: We propose using an untrained U-net in conjunction with a novel residual back projection to minimize an objective function and achieve high-accuracy reconstruction. In each iteration, the weights of the untrained U-net are optimized, and the output of the U-net in the current iteration is used to update the input of the U-net in the next iteration through the aforementioned RBP connection. Results: Experimental results demonstrate that the RBP-DIP framework offers improvements over other state-of-the-art conventional IR methods, as well as pre-trained and untrained models with similar network structures under multiple conditions. These improvements are particularly significant in the few-view, limited-angle, and low-dose imaging configurations. Conclusions: Applying to both parallel and fan beam X-ray imaging, our framework shows significant improvement under multiple conditions. Furthermore, the proposed framework requires no training data and can be adjusted on-demand to adapt to different conditions (e.g. noise level, geometry, and imaged object).

eess.IV↗

arXiv2022

A Global Constraint to Improve CT Reconstruction Under Non-Ideal Conditions

Background and Objective: The strong demand for medical imaging applications leads to the popularity of the CT reconstruction problem. Researchers proposed multiple constraints to tackle none ideal factors in CT reconstruction such as sparse-view, limited-angle, and low-dose conditions. Most of these constraints such as total variation are local constraints focusing on the relationship between a pixel and its neighbors. In this paper, we propose a new constraint utilizing the global prior of CT images to greatly reduce the streak artifacts and further improve the reconstruction accuracy. Methods: A CT image of the human body contains a limited number of different types of tissues, so pixels in CT images can be grouped into several groups according to their corresponding types. In our work, we focus on the composition classification for individual pixels and utilize it as a global prior, which differs from priors utilized by most current constraints. We propose segmenting pixels based on their gray levels during the reconstruction process, and forcing pixels in the same group to have similar gray levels. Results: Our experiments on the Shepp-Logan phantom and two real CT images from different benchmarks show that the proposed constraint can help the conventional local constraints further improve the reconstruction results under sparse-view, limited-angle, and low-dose conditions. Conclusions: Different from most current constraints focusing on the local prior, our proposed constraint only utilizes the global prior of CT images. In that case, our proposed constraint can collaborate with most local constraints and improve the reconstruction quality significantly. Furthermore, the proposed constraint also has the potential for further improvement, as the composition classification can be done with some more delicate methods, such as neural network related semantic segmentation algorithms.

eess.IV↗

arXiv2021

Kaczmarz and Gauss-Seidel Algorithms with Volume Sampling

The method of Alternating Projections (AP) is a fundamental iterative technique with applications to problems in machine learning, optimization and signal processing. Examples include the Gauss-Seidel algorithm which is used to solve large-scale regression problems and the Kaczmarz and projections onto convex sets (POCS) algorithms that are fundamental to iterative reconstruction. Progress has been made with regards to the questions of efficiency and rate of convergence in the randomized setting of the AP method. Here, we extend these results with volume sampling to block (batch) sizes greater than 1 and provide explicit formulas that relate the convergence rate bounds to the spectrum of the underlying system. These results, together with a trace formula and associated volume sampling, prove that convergence rates monotonically improve with larger block sizes, a feature that can not be guaranteed in general with uniform sampling (e.g., in SGD).

math.NA↗

arXiv2021

Statistical Rendering for Visualization of Red Sea Eddy Simulation Data

Analyzing the effects of ocean eddies is important in oceanology for gaining insights into transport of energy and biogeochemical particles. We present an application of statistical visualization algorithms for the analysis of the Red Sea eddy simulation ensemble. Specifically, we demonstrate the applications of statistical volume rendering and statistical Morse complex summary maps to a velocity magnitude field for studying the eddy positions in the flow dataset. In statistical volume rendering, we model per-voxel data uncertainty using noise models, such as parametric and nonparametric, and study the propagation of uncertainty into the volume rendering pipeline. In the statistical Morse complex summary maps, we derive histograms charactering uncertainty of gradient flow destinations to understand Morse complex topological variations across the ensemble. We demonstrate the utility of our statistical visualizations for an effective analysis of the potential eddy positions and their spatial uncertainty.

cs.GR↗

arXiv2020

Direct Volume Rendering with Nonparametric Models of Uncertainty

We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer function (TF) of the ground truth function when visualizing uncertain data; however, the existing framework is restricted to parametric models of uncertainty. In this paper, we address the limitations of the existing DVR framework by extending the DVR framework for nonparametric distributions. We exploit the quantile interpolation technique to derive probability distributions representing uncertainty in viewing-ray sample intensities in closed form, which allows for accurate and efficient computation. We evaluate our proposed nonparametric statistical models through qualitative and quantitative comparisons with the mean-field and parametric statistical models, such as uniform and Gaussian, as well as Gaussian mixtures. In addition, we present an extension of the state-of-the-art rendering parametric framework to 2D TFs for improved DVR classifications. We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets.

cs.GR↗

arXiv2020

Gram filtering and sinogram interpolation for pixel-basis in parallel-beam X-ray CT reconstruction

The key aspect of parallel-beam X-ray CT is forward and back projection, but its computational burden continues to be an obstacle for applications. We propose a method to improve the performance of related algorithms by calculating the Gram filter exactly and interpolating the sinogram signal optimally. In addition, the detector blur effect can be included in our model efficiently. The improvements in speed and quality for back projection and iterative reconstruction are shown in our experiments on both analytical phantoms and real CT images.

eess.IV↗

arXiv2019

A Convolutional Forward and Back-Projection Model for Fan-Beam Geometry

Iterative methods for tomographic image reconstruction have great potential for enabling high quality imaging from low-dose projection data. The computational burden of iterative reconstruction algorithms, however, has been an impediment in their adoption in practical CT reconstruction problems. We present an approach for highly efficient and accurate computation of forward model for image reconstruction in fan-beam geometry in X-ray CT. The efficiency of computations makes this approach suitable for large-scale optimization algorithms with on-the-fly, memory-less, computations of the forward and back-projection. Our experiments demonstrate the improvements in accuracy as well as efficiency of our model, specifically for first-order box splines (i.e., pixel-basis) compared to recently developed methods for this purpose, namely Look-up Table-based Ray Integration (LTRI) and Separable Footprints (SF) in 2-D.

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