arXiv subjects

Felix Lucka

Publications and source records attributed to Felix Lucka.

At least 37 records · Page 2Linked to original sources

arXiv2020

Fast ultrasonic imaging using end-to-end deep learning

Ultrasonic imaging algorithms used in many clinical and industrial applications consist of three steps: A data pre-processing, an image formation and an image post-processing step. For efficiency, image formation often relies on an approximation of the underlying wave physics. A prominent example is the Delay-And-Sum (DAS) algorithm used in reflectivity-based ultrasonic imaging. Recently, deep neural networks (DNNs) are being used for the data pre-processing and the image post-processing steps separately. In this work, we propose a novel deep learning architecture that integrates all three steps to enable end-to-end training. We examine turning the DAS image formation method into a network layer that connects data pre-processing layers with image post-processing layers that perform segmentation. We demonstrate that this integrated approach clearly outperforms sequential approaches that are trained separately. While network training and evaluation is performed only on simulated data, we also showcase the potential of our approach on real data from a non-destructive testing scenario.

eess.IV↗

arXiv2020

Deep data compression for approximate ultrasonic image formation

In many ultrasonic imaging systems, data acquisition and image formation are performed on separate computing devices. Data transmission is becoming a bottleneck, thus, efficient data compression is essential. Compression rates can be improved by considering the fact that many image formation methods rely on approximations of wave-matter interactions, and only use the corresponding part of the data. Tailored data compression could exploit this, but extracting the useful part of the data efficiently is not always trivial. In this work, we tackle this problem using deep neural networks, optimized to preserve the image quality of a particular image formation method. The Delay-And-Sum (DAS) algorithm is examined which is used in reflectivity-based ultrasonic imaging. We propose a novel encoder-decoder architecture with vector quantization and formulate image formation as a network layer for end-to-end training. Experiments demonstrate that our proposed data compression tailored for a specific image formation method obtains significantly better results as opposed to compression agnostic to subsequent imaging. We maintain high image quality at much higher compression rates than the theoretical lossless compression rate derived from the rank of the linear imaging operator. This demonstrates the great potential of deep ultrasonic data compression tailored for a specific image formation method.

eess.IV↗

arXiv2020

Atomic Super-Resolution Tomography

We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called discrete tomography confines the atom locations to a coarse spatial grid, which is inspired by the physical a priori knowledge that atoms in a crystalline solid tend to form regular lattices. Although this constraint has proven to be powerful for solving this very under-determined inverse problem in many cases, its key limitation is that, in practice, defects may occur that cause atoms to deviate from regular lattice positions. Here we propose a grid-free discrete tomography algorithm that allows for continuous deviations of the atom locations similar to super-resolution approaches for microscopy. The new formulation allows us to define atomic interaction potentials explicitly, which results in a both meaningful and powerful incorporation of the available physical a priori knowledge about the crystal's properties. In computational experiments, we compare the proposed grid-free method to established grid-based approaches and show that our approach can indeed recover the atom positions more accurately for common lattice defects.

math.NA↗

arXiv2020

Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast

Ultrasound Tomography has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional ultrasound tomography, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray ultrasound tomography in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and three robust, accurate, and efficient ray-linking algorithms are formulated and demonstrated. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions.

physics.comp-ph↗

arXiv2020

3D deformable registration of longitudinal abdominopelvic CT images using unsupervised deep learning

This study investigates the use of the unsupervised deep learning framework VoxelMorph for deformable registration of longitudinal abdominopelvic CT images acquired in patients with bone metastases from breast cancer. The CT images were refined prior to registration by automatically removing the CT table and all other extra-corporeal components. To improve the learning capabilities of VoxelMorph when only a limited amount of training data is available, a novel incremental training strategy is proposed based on simulated deformations of consecutive CT images. In a 4-fold cross-validation scheme, the incremental training strategy achieved significantly better registration performance compared to training on a single volume. Although our deformable image registration method did not outperform iterative registration using NiftyReg (considered as a benchmark) in terms of registration quality, the registrations were approximately 300 times faster. This study showed the feasibility of deep learning based deformable registration of longitudinal abdominopelvic CT images via a novel incremental training strategy based on simulated deformations.

eess.IV↗

arXiv2019

A Cone-Beam X-Ray CT Data Collection designed for Machine Learning

Unlike previous works, this open data collection consists of X-ray cone-beam (CB) computed tomography (CT) datasets specifically designed for machine learning applications and high cone-angle artefact reduction. Forty-two walnuts were scanned with a laboratory X-ray set-up to provide not only data from a single object but from a class of objects with natural variability. For each walnut, CB projections on three different source orbits were acquired to provide CB data with different cone angles as well as being able to compute artefact-free, high-quality ground truth images from the combined data that can be used for supervised learning. We provide the complete image reconstruction pipeline: raw projection data, a description of the scanning geometry, pre-processing and reconstruction scripts using open software, and the reconstructed volumes. Due to this, the dataset can not only be used for high cone-angle artefact reduction but also for algorithm development and evaluation for other tasks, such as image reconstruction from limited or sparse-angle (low-dose) scanning, super resolution, or segmentation.

eess.IV↗

arXiv2018

A Multi-channel DART Algorithm

Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute accurate reconstructions from highly limited projection data. For cases where the allowed intensity values in the reconstruction are known a priori, the discrete algebraic reconstruction technique (DART) has shown to yield accurate reconstructions from few projections. However, a key limitation is that the benefit of DART diminishes as the number of different materials increases. Many tomographic imaging techniques can simultaneously record tomographic data at multiple channels, each corresponding to a different weighting of the materials in the object. Whenever projection data from more than one channel is available, this additional information can potentially be exploited by the reconstruction algorithm. In this paper we present Multi-Channel DART (MC-DART), which deals effectively with multi-channel data. This class of algorithms is a generalization of DART to multiple channels and combines the information for each separate channel-reconstruction in a multi-channel segmentation step. We demonstrate that in a range of simulation experiments, MC-DART is capable of producing more accurate reconstructions compared to single-channel DART.

cs.CV↗

arXiv2018

Approximate k-space models and Deep Learning for fast photoacoustic reconstruction

We present a framework for accelerated iterative reconstructions using a fast and approximate forward model that is based on k-space methods for photoacoustic tomography. The approximate model introduces aliasing artefacts in the gradient information for the iterative reconstruction, but these artefacts are highly structured and we can train a CNN that can use the approximate information to perform an iterative reconstruction. We show feasibility of the method for human in-vivo measurements in a limited-view geometry. The proposed method is able to produce superior results to total variation reconstructions with a speed-up of 32 times.

cs.CV↗

arXiv2018

Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion Estimation

A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: images with good spatial resolution and contrast can be obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning systems if sparsity-constrained image reconstruction techniques such as total variation regularization are used. Now, we show how a further increase of image quality can be achieved for imaging dynamic processes in living tissue (4D PAT). The key idea is to exploit the additional temporal redundancy of the data by coupling the previously used spatial image reconstruction models with sparsity-constrained motion estimation models. While simulated data from a two-dimensional numerical phantom will be used to illustrate the main properties of this recently developed joint-image-reconstruction-and-motion-estimation framework, measured data from a dynamic experimental phantom will also be used to demonstrate their potential for challenging, large-scale, real-world, three-dimensional scenarios. The latter only becomes feasible if a carefully designed combination of tailored optimization schemes is employed, which we describe and examine in more detail.

math.NA↗

arXiv2018

Real-time Cardiovascular MR with Spatio-temporal Artifact Suppression using Deep Learning - Proof of Concept in Congenital Heart Disease

PURPOSE: Real-time assessment of ventricular volumes requires high acceleration factors. Residual convolutional neural networks (CNN) have shown potential for removing artifacts caused by data undersampling. In this study we investigated the effect of different radial sampling patterns on the accuracy of a CNN. We also acquired actual real-time undersampled radial data in patients with congenital heart disease (CHD), and compare CNN reconstruction to Compressed Sensing (CS). METHODS: A 3D (2D plus time) CNN architecture was developed, and trained using 2276 gold-standard paired 3D data sets, with 14x radial undersampling. Four sampling schemes were tested, using 169 previously unseen 3D 'synthetic' test data sets. Actual real-time tiny Golden Angle (tGA) radial SSFP data was acquired in 10 new patients (122 3D data sets), and reconstructed using the 3D CNN as well as a CS algorithm; GRASP. RESULTS: Sampling pattern was shown to be important for image quality, and accurate visualisation of cardiac structures. For actual real-time data, overall reconstruction time with CNN (including creation of aliased images) was shown to be more than 5x faster than GRASP. Additionally, CNN image quality and accuracy of biventricular volumes was observed to be superior to GRASP for the same raw data. CONCLUSION: This paper has demonstrated the potential for the use of a 3D CNN for deep de-aliasing of real-time radial data, within the clinical setting. Clinical measures of ventricular volumes using real-time data with CNN reconstruction are not statistically significantly different from the gold-standard, cardiac gated, BH techniques.

cs.CV↗

arXiv2018

A hierarchical Bayesian perspective on majorization-minimization for non-convex sparse regression: application to M/EEG source imaging

Majorization-minimization (MM) is a standard iterative optimization technique which consists in minimizing a sequence of convex surrogate functionals. MM approaches have been particularly successful to tackle inverse problems and statistical machine learning problems where the regularization term is a sparsity-promoting concave function. However, due to non-convexity, the solution found by MM depends on its initialization. Uniform initialization is the most natural and often employed strategy as it boils down to penalizing all coefficients equally in the first MM iteration. Yet, this arbitrary choice can lead to unsatisfactory results in severely under-determined inverse problems such as source imaging with magneto- and electro-encephalography (M/EEG). The framework of hierarchical Bayesian modeling (HBM) is an alternative approach to encode sparsity. This work shows that for certain hierarchical models, a simple alternating scheme to compute fully Bayesian maximum a posteriori (MAP) estimates leads to the exact same sequence of updates as a standard MM strategy (cf. the Adaptive Lasso). With this parallel outlined, we show how to improve upon these MM techniques by probing the multimodal posterior density using Markov Chain Monte-Carlo (MCMC) techniques. Firstly, we show that these samples can provide well-informed initializations that help MM schemes to reach better local minima. Secondly, we demonstrate how it can reveal the different modes of the posterior distribution in order to explore and quantify the inherent uncertainty and ambiguity of such ill-posed inference procedure. In the context of M/EEG, each mode corresponds to a plausible configuration of neural sources, which is crucial for data interpretation, especially in clinical contexts. Results on both simulations and real datasets show how the number or the type of sensors affect the uncertainties on the estimates.

stat.AP↗

arXiv2018

Never look back - A modified EnKF method and its application to the training of neural networks without back propagation

In this work, we present a new derivative-free optimization method and investigate its use for training neural networks. Our method is motivated by the Ensemble Kalman Filter (EnKF), which has been used successfully for solving optimization problems that involve large-scale, highly nonlinear dynamical systems. A key benefit of the EnKF method is that it requires only the evaluation of the forward propagation but not its derivatives. Hence, in the context of neural networks, it alleviates the need for back propagation and reduces the memory consumption dramatically. However, the method is not a pure "black-box" global optimization heuristic as it efficiently utilizes the structure of typical learning problems. Promising first results of the EnKF for training deep neural networks have been presented recently by Kovachki and Stuart. We propose an important modification of the EnKF that enables us to prove convergence of our method to the minimizer of a strongly convex function. Our method also bears similarity with implicit filtering and we demonstrate its potential for minimizing highly oscillatory functions using a simple example. Further, we provide numerical examples that demonstrate the potential of our method for training deep neural networks.

math.NA↗

arXiv2018

Model based learning for accelerated, limited-view 3D photoacoustic tomography

Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide high resolution 3D images from restricted photoacoustic measurements. The network is designed to represent an iterative scheme and incorporates gradient information of the data fit to compensate for limited view artefacts. Due to the high complexity of the photoacoustic forward operator, we separate training and computation of the gradient information. A suitable prior for the desired image structures is learned as part of the training. The resulting network is trained and tested on a set of segmented vessels from lung CT scans and then applied to in-vivo photoacoustic measurement data.

cs.CV↗

arXiv2017

Risk Estimators for Choosing Regularization Parameters in Ill-Posed Problems - Properties and Limitations

This paper discusses the properties of certain risk estimators recently proposed to choose regularization parameters in ill-posed problems. A simple approach is Stein's unbiased risk estimator (SURE), which estimates the risk in the data space, while a recent modification (GSURE) estimates the risk in the space of the unknown variable. It seems intuitive that the latter is more appropriate for ill-posed problems, since the properties in the data space do not tell much about the quality of the reconstruction. We provide theoretical studies of both estimators for linear Tikhonov regularization in a finite dimensional setting and estimate the quality of the risk estimators, which also leads to asymptotic convergence results as the dimension of the problem tends to infinity. Unlike previous papers, who studied image processing problems with a very low degree of ill-posedness, we are interested in the behavior of the risk estimators for increasing ill-posedness. Interestingly, our theoretical results indicate that the quality of the GSURE risk can deteriorate asymptotically for ill-posed problems, which is confirmed by a detailed numerical study. The latter shows that in many cases the GSURE estimator leads to extremely small regularization parameters, which obviously cannot stabilize the reconstruction. Similar but less severe issues with respect to robustness also appear for the SURE estimator, which in comparison to the rather conservative discrepancy principle leads to the conclusion that regularization parameter choice based on unbiased risk estimation is not a reliable procedure for ill-posed problems. A similar numerical study for sparsity regularization demonstrates that the same issue appears in nonlinear variational regularization approaches.

math.ST↗

arXiv2017

Bayesian Modelling of Skull Conductivity Uncertainties in EEG Source Imaging

Knowing the correct skull conductivity is crucial for the accuracy of EEG source imaging, but unfortunately, its true value, which is inter- and intra-individually varying, is difficult to determine. In this paper, we propose a statistical method based on the Bayesian approximation error approach to compensate for source imaging errors related to erroneous skull conductivity. We demonstrate the potential of the approach by simulating EEG data of focal source activity and using the dipole scan algorithm and a sparsity promoting prior to reconstruct the underlying sources. The results suggest that the greatest improvements with the proposed method can be achieved when the focal sources are close to the skull.

physics.med-ph↗

arXiv2016

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.

math.NA↗

arXiv2016

On the Adjoint Operator in Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.

math.NA↗

arXiv2016

Fast Gibbs sampling for high-dimensional Bayesian inversion

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures, this can be a significant advantage. Alongside theoretical progress, various new computational techniques allow to sample very high dimensional posterior distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior sampler was developed for linear inverse problems with $\ell_1$-type priors. In this article, we extend this single component Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general $\ell_p^q$ priors with additional hard constraints. Besides a fast computation of the conditional, single component densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography (CT) data with the popular isotropic total variation (TV) prior.

math.NA↗