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Markus Haltmeier

Publications and source records attributed to Markus Haltmeier.

At least 37 records · Page 2Linked to original sources
arXiv2024

A lightweight residual network for unsupervised deformable image registration

Accurate volumetric image registration is highly relevant for clinical routines and computer-aided medical diagnosis. Recently, researchers have begun to use transformers in learning-based methods for medical image registration, and have achieved remarkable success. Due to the strong global modeling capability, Transformers are considered a better option than convolutional neural networks (CNNs) for registration. However, they use bulky models with huge parameter sets, which require high computation edge devices for deployment as portable devices or in hospitals. Transformers also need a large amount of training data to produce significant results, and it is often challenging to collect suitable annotated data. Although existing CNN-based image registration can offer rich local information, their global modeling capability is poor for handling long-distance information interaction and limits registration performance. In this work, we propose a CNN-based registration method with an enhanced receptive field, a low number of parameters, and significant results on a limited training dataset. For this, we propose a residual U-Net with embedded parallel dilated-convolutional blocks to enhance the receptive field. The proposed method is evaluated on inter-patient and atlas-based datasets. We show that the performance of the proposed method is comparable and slightly better than transformer-based methods by using only $\SI{1.5}{\percent}$ of its number of parameters.

cs.CV↗
arXiv2024

Full Field Inversion of the Attenuated Wave Equation: Theory and Numerical Inversion

Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contrast, the measured data from the recently invented full-field PAT is the Radon transform of the solution of the wave equation on a spatial domain at a single instant in time. While reconstruction using classical PAT data has been extensively studied, not much is known about the full-field PAT problem. In this paper, we study full-field photoacoustic tomography with spatially variable sound speed and spatially variable damping. In particular, we prove the uniqueness and stability of the associated single-time full-field wave inversion problem and develop algorithms for its numerical inversion using iterative and variational regularization methods. Numerical simulations are presented for both full-angle and limited-angle data cases

math.NA↗
arXiv2024

Self2Seg: Single-Image Self-Supervised Joint Segmentation and Denoising

We develop Self2Seg, a self-supervised method for the joint segmentation and denoising of a single image. To this end, we combine the advantages of variational segmentation with self-supervised deep learning. One major benefit of our method lies in the fact, that in contrast to data-driven methods, where huge amounts of labeled samples are necessary, Self2Seg segments an image into meaningful regions without any training database. Moreover, we demonstrate that self-supervised denoising itself is significantly improved through the region-specific learning of Self2Seg. Therefore, we introduce a novel self-supervised energy functional in which denoising and segmentation are coupled in a way that both tasks benefit from each other. We propose a unified optimisation strategy and numerically show that for noisy microscopy images our proposed joint approach outperforms its sequential counterpart as well as alternative methods focused purely on denoising or segmentation.

cs.CV↗
arXiv2024

Deep Gaussian mixture model for unsupervised image segmentation

The recent emergence of deep learning has led to a great deal of work on designing supervised deep semantic segmentation algorithms. As in many tasks sufficient pixel-level labels are very difficult to obtain, we propose a method which combines a Gaussian mixture model (GMM) with unsupervised deep learning techniques. In the standard GMM the pixel values with each sub-region are modelled by a Gaussian distribution. In order to identify the different regions, the parameter vector that minimizes the negative log-likelihood (NLL) function regarding the GMM has to be approximated. For this task, usually iterative optimization methods such as the expectation-maximization (EM) algorithm are used. In this paper, we propose to estimate these parameters directly from the image using a convolutional neural network (CNN). We thus change the iterative procedure in the EM algorithm replacing the expectation-step by a gradient-step with regard to the networks parameters. This means that the network is trained to minimize the NLL function of the GMM which comes with at least two advantages. As once trained, the network is able to predict label probabilities very quickly compared with time consuming iterative optimization methods. Secondly, due to the deep image prior our method is able to partially overcome one of the main disadvantages of GMM, which is not taking into account correlation between neighboring pixels, as it assumes independence between them. We demonstrate the advantages of our method in various experiments on the example of myocardial infarct segmentation on multi-sequence MRI images.

cs.CV↗
arXiv2024

Sparse2Inverse: Self-supervised inversion of sparse-view CT data

Sparse-view computed tomography (CT) enables fast and low-dose CT imaging, an essential feature for patient-save medical imaging and rapid non-destructive testing. In sparse-view CT, only a few projection views are acquired, causing standard reconstructions to suffer from severe artifacts and noise. To address these issues, we propose a self-supervised image reconstruction strategy. Specifically, in contrast to the established Noise2Inverse, our proposed training strategy uses a loss function in the projection domain, thereby bypassing the otherwise prescribed nullspace component. We demonstrate the effectiveness of the proposed method in reducing stripe-artifacts and noise, even from highly sparse data.

eess.IV↗
arXiv2024

Convergence of non-linear diagonal frame filtering for regularizing inverse problems

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization techniques have been proposed. In particular, the use of filtered diagonal frame decompositions has proven to be effective and computationally efficient. However, existing convergence analysis applies only to linear filters and a few non-linear filters such as soft thresholding. In this paper, we analyze filtered diagonal frame decompositions with general non-linear filters. In particular, our results generalize SVD-based spectral filtering from linear to non-linear filters as a special case. As a first approach, we establish a connection between non-linear diagonal frame filtering and variational regularization, allowing us to use results from variational regularization to derive the convergence of non-linear spectral filtering. In the second approach, as our main theoretical results, we relax the assumptions involved in the variational case while still deriving convergence. Furthermore, we discuss connections between non-linear filtering and plug-and-play regularization and explore potential benefits of this relationship.

math.NA↗
arXiv2024

Design, Implementation and Analysis of a Compressed Sensing Photoacoustic Projection Imaging System

Significance: Compressed sensing (CS) uses special measurement designs combined with powerful mathematical algorithms to reduce the amount of data to be collected while maintaining image quality. This is relevant to almost any imaging modality, and in this paper we focus on CS in photoacoustic projection imaging (PAPI) with integrating line detectors (ILDs). Aim: Our previous research involved rather general CS measurements, where each ILD can contribute to any measurement. In the real world, however, the design of CS measurements is subject to practical constraints. In this research, we aim at a CS-PAPI system where each measurement involves only a subset of ILDs, and which can be implemented in a cost-effective manner. Approach: We extend the existing PAPI with a self-developed CS unit. The system provides structured CS matrices for which the existing recovery theory cannot be applied directly. A random search strategy is applied to select the CS measurement matrix within this class for which we obtain exact sparse recovery. Results: We implement a CS PAPI system for a compression factor of $4:3$, where specific measurements are made on separate groups of 16 ILDs. We algorithmically design optimal CS measurements that have proven sparse CS capabilities. Numerical experiments are used to support our results. Conclusions: CS with proven sparse recovery capabilities can be integrated into PAPI, and numerical results support this setup. Future work will focus on applying it to experimental data and utilizing data-driven approaches to enhance the compression factor and generalize the signal class.

cs.CV↗
arXiv2024

Derivative-Free iterative One-Step Reconstruction for Multispectral CT

Image reconstruction in Multispectral Computed Tomography (MSCT) requires solving a challenging nonlinear inverse problem, commonly tackled via iterative optimization algorithms. Existing methods necessitate computing the derivative of the forward map and potentially its regularized inverse. In this work, we present a simple yet highly effective algorithm for MSCT image reconstruction, utilizing iterative update mechanisms that leverage the full forward model in the forward step and a derivative-free adjoint problem. Our approach demonstrates both fast convergence and superior performance compared to existing algorithms, making it an interesting candidate for future work. We also discuss further generalizations of our method and its combination with additional regularization and other data discrepancy terms.

math.NA↗
arXiv2024

ECALL: Expectation-calibrated learning for unsupervised blind deconvolution

Blind deconvolution aims to recover an original image from a blurred version in the case where the blurring kernel is unknown. It has wide applications in diverse fields such as astronomy, microscopy, and medical imaging. Blind deconvolution is a challenging ill-posed problem that suffers from significant non-uniqueness. Solution methods therefore require the integration of appropriate prior information. Early approaches rely on hand-crafted priors for the original image and the kernel. Recently, deep learning methods have shown excellent performance in addressing this challenge. However, most existing learning methods for blind deconvolution require a paired dataset of original and blurred images, which is often difficult to obtain. In this paper, we present a novel unsupervised learning approach named ECALL (Expectation-CALibrated Learning) that uses separate unpaired collections of original and blurred images. Key features of the proposed loss function are cycle consistency involving the kernel and associated reconstruction operator, and terms that use expectation values of data distributions to obtain information about the kernel. Numerical results are used to support ECALL.

math.NA↗
arXiv2023

Three-dimensional Bone Image Synthesis with Generative Adversarial Networks

Medical image processing has been highlighted as an area where deep learning-based models have the greatest potential. However, in the medical field in particular, problems of data availability and privacy are hampering research progress and thus rapid implementation in clinical routine. The generation of synthetic data not only ensures privacy, but also allows to \textit{draw} new patients with specific characteristics, enabling the development of data-driven models on a much larger scale. This work demonstrates that three-dimensional generative adversarial networks (GANs) can be efficiently trained to generate high-resolution medical volumes with finely detailed voxel-based architectures. In addition, GAN inversion is successfully implemented for the three-dimensional setting and used for extensive research on model interpretability and applications such as image morphing, attribute editing and style mixing. The results are comprehensively validated on a database of three-dimensional HR-pQCT instances representing the bone micro-architecture of the distal radius.

eess.IV↗
arXiv2023

Breaking the Resolution limit in Photoacoustic Imaging using Positivity and Sparsity

In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can nevertheless be overcome and include some concrete technological applications. Describing diffusion as a random walk, one insight is that such a stochastic process involves not only a Gaussian spread of the mean values in space, with the variance proportional to the diffusion time, but also temporal and spatial fluctuations around these mean values. All these fluctuations strongly influence the image reconstruction immediately after the short heating pulse. The Gaussian spread of the mean values in space increases the entropy, while the fluctuations lead to a loss of information that blurs the reconstruction of the initial temperature distribution and can be described mathematically by a spatial convolution with a Gaussian thermal point-spread-function (PSF). The information loss turns out to be equal to the mean entropy increase and limits the spatial resolution proportional to the depth of the imaged subsurface structures. This principal resolution limit can only be overcome by including additional information such as sparsity or positivity. Prior information can be also included by using a deep neural network with a finite degrees of freedom and trained on a specific class of image examples for image reconstruction

math.NA↗
arXiv2023

Heat diffusion blurs photothermal images with increasing depth

In this tutorial, we aim to directly recreate some of our "aha" moments when exploring the impact of heat diffusion on the spatial resolution limit of photothermal imaging. Our objective is also to communicate how this physical limit can nevertheless be overcome and include some concrete technological applications. Describing diffusion as a random walk, one insight is that such a stochastic process involves not only a Gaussian spread of the mean values in space, with the variance proportional to the diffusion time, but also temporal and spatial fluctuations around these mean values. All these fluctuations strongly influence the image reconstruction immediately after the short heating pulse. The Gaussian spread of the mean values in space increases the entropy, while the fluctuations lead to a loss of information that blurs the reconstruction of the initial temperature distribution and can be described mathematically by a spatial convolution with a Gaussian thermal point-spread-function (PSF). The information loss turns out to be equal to the mean entropy increase and limits the spatial resolution proportional to the depth of the imaged subsurface structures. This principal resolution limit can only be overcome by including additional information such as sparsity or positivity. Prior information can be also included by using a deep neural network with a finite degrees of freedom and trained on a specific class of image examples for image reconstruction.

math.NA↗
arXiv2023

Superiorized Regularization of Inverse Problems

Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative regularization methods. Superiorization is a heuristic approach that can steer basic iterative algorithms to have small value of certain regularization functional while keeping the algorithms simplicity and computational efforts, but is able to account for additional prior information. In this note, we combine the superiorization methodology with iterative regularization methods and show that the superiorized version of the scheme yields again a regularization method, however accounting for different prior information.

math.NA↗
arXiv2023

Sampling and resolution in sparse view photoacoustic tomography

We investigate resolution in photoacoustic tomography (PAT). Using Shannon theory, we investigate the theoretical resolution limit of sparse view PAT theoretically, and empirically demonstrate that all reconstruction methods used exceed this limit.

math.NA↗
arXiv2023

Lifting-based variational multiclass segmentation algorithm: design, convergence analysis, and implementation with applications in medical imaging

We propose, analyze and realize a variational multiclass segmentation scheme that partitions a given image into multiple regions exhibiting specific properties. Our method determines multiple functions that encode the segmentation regions by minimizing an energy functional combining information from different channels. Multichannel image data can be obtained by lifting the image into a higher dimensional feature space using specific multichannel filtering or may already be provided by the imaging modality under consideration, such as an RGB image or multimodal medical data. Experimental results show that the proposed method performs well in various scenarios. In particular, promising results are presented for two medical applications involving classification of brain abscess and tumor growth, respectively. As main theoretical contributions, we prove the existence of global minimizers of the proposed energy functional and show its stability and convergence with respect to noisy inputs. In particular, these results also apply to the special case of binary segmentation, and these results are also novel in this particular situation.

cs.CV↗
arXiv2023

Data-proximal null-space networks for inverse problems

Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning based approaches have shown remarkable practical performance. However, the theoretical foundations of learning-based methods in the context of regularization are still underexplored. In this paper, we propose a general framework that addresses the current gap between learning-based methods and regularization strategies. In particular, our approach emphasizes the crucial role of data consistency in the solution of inverse problems and introduces the concept of data-proximal null-space networks as a key component for their solution. We provide a complete convergence analysis by extending the concept of regularizing null-space networks with data proximity in the visual part. We present numerical results for limited-view computed tomography to illustrate the validity of our framework.

math.NA↗
arXiv2023

Translation invariant diagonal frame decomposition for the Radon transform

In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD). First, we review the concept of a TI-DFD for general linear operators and the corresponding filter-based regularization. We then introduce the TI-DFD for the Radon transform on $L^2(\R^2)$ and provide an exemplary construction using the TI wavelet transform. Presented numerical results clearly demonstrate the benefits of our approach over non-translation invariant counterparts.

math.NA↗