459 research outputs found
Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing
Current 3D photoacoustic tomography (PAT) systems offer either high image
quality or high frame rates but are not able to deliver high spatial and
temporal resolution simultaneously, which limits their ability to image dynamic
processes in living tissue. A particular example is the planar Fabry-Perot (FP)
scanner, which yields high-resolution images but takes several minutes to
sequentially map the photoacoustic field on the sensor plane, point-by-point.
However, as the spatio-temporal complexity of many absorbing tissue structures
is rather low, the data recorded in such a conventional, regularly sampled
fashion is often highly redundant. We demonstrate that combining variational
image reconstruction methods using spatial sparsity constraints with the
development of novel PAT acquisition systems capable of sub-sampling the
acoustic wave field can dramatically increase the acquisition speed while
maintaining a good spatial resolution: First, we describe and model two general
spatial sub-sampling schemes. Then, we discuss how to implement them using the
FP scanner and demonstrate the potential of these novel compressed sensing PAT
devices through simulated data from a realistic numerical phantom and through
measured data from a dynamic experimental phantom as well as from in-vivo
experiments. Our results show that images with good spatial resolution and
contrast can be obtained from highly sub-sampled PAT data if variational image
reconstruction methods that describe the tissues structures with suitable
sparsity-constraints are used. In particular, we examine the use of total
variation regularization enhanced by Bregman iterations. These novel
reconstruction strategies offer new opportunities to dramatically increase the
acquisition speed of PAT scanners that employ point-by-point sequential
scanning as well as reducing the channel count of parallelized schemes that use
detector arrays.Comment: submitted to "Physics in Medicine and Biology
Sinogram Restoration for Low-Dosed X-Ray Computed Tomography Using Fractional-Order Perona-Malik Diffusion
Existing integer-order Nonlinear Anisotropic Diffusion (NAD) used in noise suppressing will produce undesirable staircase effect or speckle effect. In this paper, we propose a new scheme, named Fractal-order Perona-Malik Diffusion (FPMD), which replaces the integer-order derivative of the Perona-Malik (PM) Diffusion with the fractional-order derivative using G-L fractional derivative. FPMD, which is a interpolation between integer-order Nonlinear Anisotropic Diffusion (NAD) and fourth-order partial differential equations, provides a more flexible way to balance the noise reducing and anatomical details preserving. Smoothing results for phantoms and real sinograms show that FPMD with suitable parameters can suppress the staircase effects and speckle effects efficiently. In addition, FPMD also has a good performance in visual quality and root mean square errors (RMSE)
Connecting mathematical models for image processing and neural networks
This thesis deals with the connections between mathematical models for image processing and deep learning. While data-driven deep learning models such as neural networks are flexible and well performing, they are often used as a black box. This makes it hard to provide theoretical model guarantees and scientific insights. On the other hand, more traditional, model-driven approaches such as diffusion, wavelet shrinkage, and variational models offer a rich set of mathematical foundations. Our goal is to transfer these foundations to neural networks. To this end, we pursue three strategies. First, we design trainable variants of traditional models and reduce their parameter set after training to obtain transparent and adaptive models. Moreover, we investigate the architectural design of numerical solvers for partial differential equations and translate them into building blocks of popular neural network architectures. This yields criteria for stable networks and inspires novel design concepts. Lastly, we present novel hybrid models for inpainting that rely on our theoretical findings. These strategies provide three ways for combining the best of the two worlds of model- and data-driven approaches. Our work contributes to the overarching goal of closing the gap between these worlds that still exists in performance and understanding.Gegenstand dieser Arbeit sind die ZusammenhĂ€nge zwischen mathematischen Modellen zur Bildverarbeitung und Deep Learning. WĂ€hrend datengetriebene Modelle des Deep Learning wie z.B. neuronale Netze flexibel sind und gute Ergebnisse liefern, werden sie oft als Black Box eingesetzt. Das macht es schwierig, theoretische Modellgarantien zu liefern und wissenschaftliche Erkenntnisse zu gewinnen. Im Gegensatz dazu bieten traditionellere, modellgetriebene AnsĂ€tze wie Diffusion, Wavelet Shrinkage und VariationsansĂ€tze eine FĂŒlle von mathematischen Grundlagen. Unser Ziel ist es, diese auf neuronale Netze zu ĂŒbertragen. Zu diesem Zweck verfolgen wir drei Strategien. ZunĂ€chst entwerfen wir trainierbare Varianten von traditionellen Modellen und reduzieren ihren Parametersatz, um transparente und adaptive Modelle zu erhalten. AuĂerdem untersuchen wir die Architekturen von numerischen Lösern fĂŒr partielle Differentialgleichungen und ĂŒbersetzen sie in Bausteine von populĂ€ren neuronalen Netzwerken. Daraus ergeben sich Kriterien fĂŒr stabile Netzwerke und neue Designkonzepte. SchlieĂlich prĂ€sentieren wir neuartige hybride Modelle fĂŒr Inpainting, die auf unseren theoretischen Erkenntnissen beruhen. Diese Strategien bieten drei Möglichkeiten, das Beste aus den beiden Welten der modell- und datengetriebenen AnsĂ€tzen zu vereinen. Diese Arbeit liefert einen Beitrag zum ĂŒbergeordneten Ziel, die LĂŒcke zwischen den zwei Welten zu schlieĂen, die noch in Bezug auf Leistung und ModellverstĂ€ndnis besteht.ERC Advanced Grant INCOVI
Scaling Multidimensional Inference for Big Structured Data
In information technology, big data is a collection of data sets so large and complex that it becomes difficult to process using traditional data processing applications [151]. In a
world of increasing sensor modalities, cheaper storage, and more data oriented questions, we are quickly passing the limits of tractable computations using traditional statistical analysis
methods. Methods which often show great results on simple data have difficulties processing complicated multidimensional data. Accuracy alone can no longer justify unwarranted memory
use and computational complexity. Improving the scaling properties of these methods for multidimensional data is the only way to make these methods relevant. In this work we explore methods for improving the scaling properties of parametric and nonparametric
models. Namely, we focus on the structure of the data to lower the complexity of a specific family of problems. The two types of structures considered in this work are distributive
optimization with separable constraints (Chapters 2-3), and scaling Gaussian processes for multidimensional lattice input (Chapters 4-5). By improving the scaling of these methods, we can expand their use to a wide range of applications which were previously intractable
open the door to new research questions
VisualPDE: rapid interactive simulations of partial differential equations
Computing has revolutionised the study of complex nonlinear systems, both by
allowing us to solve previously intractable models and through the ability to
visualise solutions in different ways. Using ubiquitous computing
infrastructure, we provide a means to go one step further in using computers to
understand complex models through instantaneous and interactive exploration.
This ubiquitous infrastructure has enormous potential in education, outreach
and research. Here, we present VisualPDE, an online, interactive solver for a
broad class of 1D and 2D partial differential equation (PDE) systems. Abstract
dynamical systems concepts such as symmetry-breaking instabilities, subcritical
bifurcations and the role of initial data in multistable nonlinear models
become much more intuitive when you can play with these models yourself, and
immediately answer questions about how the system responds to changes in
parameters, initial conditions, boundary conditions or even spatiotemporal
forcing. Importantly, VisualPDE is freely available, open source and highly
customisable. We give several examples in teaching, research and knowledge
exchange, providing high-level discussions of how it may be employed in
different settings. This includes designing web-based course materials
structured around interactive simulations, or easily crafting specific
simulations that can be shared with students or collaborators via a simple URL.
We envisage VisualPDE becoming an invaluable resource for teaching and research
in mathematical biology and beyond. We also hope that it inspires other efforts
to make mathematics more interactive and accessible.Comment: 19 pages, 7 figures. This is a companion paper to the website
https://visualpde.com
Nonlinear Adaptive Diffusion Models for Image Denoising
Most of digital image applications demand on high image quality. Unfortunately, images often are degraded by noise during the formation, transmission, and recording processes. Hence, image denoising is an essential processing step preceding visual and automated analyses. Image denoising methods can reduce image contrast, create block or ring artifacts in the process of denoising. In this dissertation, we develop high performance non-linear diffusion based image denoising methods, capable to preserve edges and maintain high visual quality. This is attained by different approaches: First, a nonlinear diffusion is presented with robust M-estimators as diffusivity functions. Secondly, the knowledge of textons derived from Local Binary Patterns (LBP) which unify divergent statistical and structural models of the region analysis is utilized to adjust the time step of diffusion process. Next, the role of nonlinear diffusion which is adaptive to the local context in the wavelet domain is investigated, and the stationary wavelet context based diffusion (SWCD) is developed for performing the iterative shrinkage. Finally, we develop a locally- and feature-adaptive diffusion (LFAD) method, where each image patch/region is diffused individually, and the diffusivity function is modified to incorporate the Inverse Difference Moment as a local estimate of the gradient. Experiments have been conducted to evaluate the performance of each of the developed method and compare it to the reference group and to the state-of-the-art methods
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