WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution

Altekrüger, Fabian; Hertrich, Johannes

doi:10.1137/22m1496542

Cited by 7 publications

(6 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, it can mitigate GPU memory exhaustion and reduce training time. This approach has proven successful in various image tasks such as superresolution and denoising [47,5].…”

Section: Kernel Classesmentioning

confidence: 99%

ASTRA kernelkit: GPU-accelerated projectors for computed tomography using cupy

Graas,

Jan Palenstijn,

van Werkhoven

et al. 2024

AMMC

View full text Add to dashboard Cite

New computed tomography (CT) algorithms are commonly developed in high-level programming languages, such as Python or MATLAB, while low-level languages are used to support their computation-intensive operations. In the past decade, graphics processing units (GPUs) have become the de-facto standard for large parallel computations in areas such as computational imaging, image processing, and machine learning. Our fast-and-flexible CT reconstruction software, ASTRA Toolbox, therefore already implemented tomographic projectors, i.e., the core computational operations modeling the X-ray physics, using NVIDIA CUDA (Compute Unified Device Architecture), a low-level platform for computation on GPUs. However, the Python-C++ language barrier prevents high-level Python users from modifying these lowlevel projectors, and, as a consequence, research into new tomographic algorithms is more complex and time-consuming than necessary. With the ASTRA KernelKit, we lifted tomographic projectors to Python and leveraged CuPy, a numerical software like NumPy and SciPy that exposes CUDA to Python, to obtain a fine-grained control over their efficiency and implementation. In this article, we introduced our software and illustrated its importance for highperformance and data-driven applications using examples from deep learning, real-time X-ray CT, and kernel tuning.

show abstract

“…For example, it can mitigate GPU memory exhaustion and reduce training time. This approach has proven successful in various image tasks such as superresolution and denoising [47,5].…”

Section: Kernel Classesmentioning

confidence: 99%

ASTRA kernelkit: GPU-accelerated projectors for computed tomography using cupy

Graas,

Jan Palenstijn,

van Werkhoven

et al. 2024

AMMC

View full text Add to dashboard Cite

show abstract

“…We will derive an EM algorithm for this problem, where the hidden variable is given by the ground truth random variable X. In particular, we will deal with the noise model (2). Here the parameter θ = (a, b) can be updated in the M-step analytically.…”

Section: Parameter Estimation In Bayesian Inverse Problemsmentioning

confidence: 99%

“…see [2,3,40] for a detailed explanation and applications. In order to evaluate these terms we have to be able to evaluate the prior density p X as well as the conditional densities p Y θ (r) |X=x (y), which contains the forward operator and the noise model for given parameters θ (r) .…”

Section: E-step: Conditional Nfsmentioning

confidence: 99%

“…where F(x) 2 = (F i (x) 2 ) n i =1 and the identity in R n×n is given by I n . For convenience we assume that the instrument noise and other sources can be described by the simple Ansatz made here.…”

Section: Introductionmentioning

confidence: 99%

“…In general different noise models may appear in the applications. The noise model equation (2) was used in several previous studies in optics [29,30,32,59] and analyzed in [19]. A similar noise model appears in analytical chemistry [58] and the study of gene expression arrays [57].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mixed noise and posterior estimation with conditional deepGEM

Hagemann,

Hertrich,

Casfor

et al. 2024

Mach. Learn.: Sci. Technol.

Self Cite

View full text Add to dashboard Cite

We develop an algorithm for jointly estimating the posterior and the noise parameters in Bayesian inverse problems, which is motivated by indirect measurements and applications from nanometrology with a mixed noise model. We propose to solve the problem by an expectation maximization (EM) algorithm. Based on the current noise parameters, we learn in the E-step a conditional normalizing flow that approximates the posterior. In the M-step, we propose to find the noise parameter updates again by an EM algorithm, which has analytical formulas. We compare the training of the conditional normalizing flow with the forward and reverse Kullback–Leibler divergence, and show that our model is able to incorporate information from many measurements, unlike previous approaches.

show abstract

Learning from small data sets: Patch‐based regularizers in inverse problems for image reconstruction

Piening,

Altekrüger,

Hertrich

et al. 2024

GAMM-Mitteilungen

View full text Add to dashboard Cite

The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep neural networks. Most of these methods require a huge amount of data and computer capacity to train the networks, which often may not be available. Our paper addresses the issue of learning from small data sets by taking patches of very few images into account. We focus on the combination of model‐based and data‐driven methods by approximating just the image prior, also known as regularizer in the variational model. We review two methodically different approaches, namely optimizing the maximum log‐likelihood of the patch distribution, and penalizing Wasserstein‐like discrepancies of whole empirical patch distributions. From the point of view of Bayesian inverse problems, we show how we can achieve uncertainty quantification by approximating the posterior using Langevin Monte Carlo methods. We demonstrate the power of the methods in computed tomography, image super‐resolution, and inpainting. Indeed, the approach provides also high‐quality results in zero‐shot super‐resolution, where only a low‐resolution image is available. The article is accompanied by a GitHub repository containing implementations of all methods as well as data examples so that the reader can get their own insight into the performance.

show abstract

WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution

Cited by 7 publications

References 33 publications

ASTRA kernelkit: GPU-accelerated projectors for computed tomography using cupy

ASTRA kernelkit: GPU-accelerated projectors for computed tomography using cupy

Mixed noise and posterior estimation with conditional deepGEM

Learning from small data sets: Patch‐based regularizers in inverse problems for image reconstruction

Contact Info

Product

Resources

About