A novel image space formalism of Fourier domain interpolation neural networks for noise propagation analysis

• URL: http://arxiv.org/abs/2402.17410v1
• Date: Tue, 27 Feb 2024 11:01:58 GMT
• Title: A novel image space formalism of Fourier domain interpolation neural networks for noise propagation analysis
• Authors: Peter Dawood, Felix Breuer, Istvan Homolya, Jannik Stebani, Maximilian Gram, Peter M. Jakob, Moritz Zaiss, Martin Blaimer
• Abstract summary: We develop an image space formalism of convolutional neural networks (CNNs) for the Fourier domain in MRI reconstructions. Inferences conducted in the image domain are quasi-identical to inferences in the k-space. The noise resilience is well characterized, as in the case of classical Parallel Imaging.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Purpose: To develop an image space formalism of multi-layer convolutional neural networks (CNNs) for Fourier domain interpolation in MRI reconstructions and analytically estimate noise propagation during CNN inference. Theory and Methods: Nonlinear activations in the Fourier domain (also known as k-space) using complex-valued Rectifier Linear Units are expressed as elementwise multiplication with activation masks. This operation is transformed into a convolution in the image space. After network training in k-space, this approach provides an algebraic expression for the derivative of the reconstructed image with respect to the aliased coil images, which serve as the input tensors to the network in the image space. This allows the variance in the network inference to be estimated analytically and to be used to describe noise characteristics. Monte-Carlo simulations and numerical approaches based on auto-differentiation were used for validation. The framework was tested on retrospectively undersampled invivo brain images. Results: Inferences conducted in the image domain are quasi-identical to inferences in the k-space, underlined by corresponding quantitative metrics. Noise variance maps obtained from the analytical expression correspond with those obtained via Monte-Carlo simulations, as well as via an auto-differentiation approach. The noise resilience is well characterized, as in the case of classical Parallel Imaging. Komolgorov-Smirnov tests demonstrate Gaussian distributions of voxel magnitudes in variance maps obtained via Monte-Carlo simulations. Conclusion: The quasi-equivalent image space formalism for neural networks for k-space interpolation enables fast and accurate description of the noise characteristics during CNN inference, analogous to geometry-factor maps in traditional parallel imaging methods.

Related papers

• Image segmentation with traveling waves in an exactly solvable recurrent neural network [71.74150501418039]
  We show that a recurrent neural network can effectively divide an image into groups according to a scene's structural characteristics. We present a precise description of the mechanism underlying object segmentation in this network. We then demonstrate a simple algorithm for object segmentation that generalizes across inputs ranging from simple geometric objects in grayscale images to natural images.
  arXiv  Detail & Related papers  (2023-11-28T16:46:44Z)
• Neural Spherical Harmonics for structurally coherent continuous representation of diffusion MRI signal [0.3277163122167433]
  We present a novel way to model diffusion magnetic resonance imaging (dMRI) datasets, that benefits from the structural coherence of the human brain. Current methods model the dMRI signal in individual voxels, disregarding the intervoxel coherence that is present. We use a neural network to parameterize a spherical harmonics series to represent the dMRI signal of a single subject from the Human Connectome Project dataset.
  arXiv  Detail & Related papers  (2023-08-16T08:28:01Z)
• SO(2) and O(2) Equivariance in Image Recognition with Bessel-Convolutional Neural Networks [63.24965775030674]
  This work presents the development of Bessel-convolutional neural networks (B-CNNs) B-CNNs exploit a particular decomposition based on Bessel functions to modify the key operation between images and filters. Study is carried out to assess the performances of B-CNNs compared to other methods.
  arXiv  Detail & Related papers  (2023-04-18T18:06:35Z)
• Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back [84.61160272624262]
  We define tangent bundle filters and tangent bundle neural networks (TNNs) based on this convolution operation. Tangent bundle filters admit a spectral representation that generalizes the ones of scalar manifold filters, graph filters and standard convolutional filters in continuous time. We numerically evaluate the effectiveness of the proposed architecture on various learning tasks.
  arXiv  Detail & Related papers  (2023-03-20T17:57:15Z)
• Tensor Factorization via Transformed Tensor-Tensor Product for Image Alignment [3.0969191504482243]
  We study the problem of a batch of linearly correlated image alignment, where the observed images are deformed by some unknown domain transformations. By stacking these images as the frontal slices of a third-order tensor, we propose to explore the low-rankness of the underlying tensor.
  arXiv  Detail & Related papers  (2022-12-12T05:52:26Z)
• Analysis of convolutional neural network image classifiers in a rotationally symmetric model [4.56877715768796]
  The rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. It is shown that least squares plug-in classifiers based on convolutional neural networks are able to circumvent the curse of dimensionality in binary image classification.
  arXiv  Detail & Related papers  (2022-05-11T13:43:13Z)
• Moment evolution equations and moment matching for stochastic image EPDiff [68.97335984455059]
  Models of image deformation allow study of time-continuous effects transforming images by deforming the image domain. Applications include medical image analysis with both population trends and random subject specific variation. We use moment approximations of the corresponding Ito diffusion to construct estimators for statistical inference in the parameters full model.
  arXiv  Detail & Related papers  (2021-10-07T11:08:11Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)
• Deep Network for Scatterer Distribution Estimation for Ultrasound Image Simulation [8.13909718726358]
  We demonstrate a convolutional neural network approach for probabilistic scatterer estimation from observed ultrasound data. In comparison with several existing approaches, we demonstrate in numerical simulations and with in-vivo images that the synthesized images from scatterer representations estimated with our approach closely match the observations.
  arXiv  Detail & Related papers  (2020-06-17T21:25:13Z)
• Geometric Approaches to Increase the Expressivity of Deep Neural Networks for MR Reconstruction [41.62169556793355]
  Deep learning approaches have been extensively investigated to reconstruct images from accelerated magnetic resonance image (MRI) acquisition. It is not clear how to choose a suitable network architecture to balance the trade-off between network complexity and performance. This paper proposes a systematic geometric approach using bootstrapping and subnetwork aggregation to increase the expressivity of the underlying neural network.
  arXiv  Detail & Related papers  (2020-03-17T14:18:37Z)
• Residual-Sparse Fuzzy $C$-Means Clustering Incorporating Morphological Reconstruction and Wavelet frames [146.63177174491082]
  Fuzzy $C$-Means (FCM) algorithm incorporates a morphological reconstruction operation and a tight wavelet frame transform. We present an improved FCM algorithm by imposing an $ell_0$ regularization term on the residual between the feature set and its ideal value. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.
  arXiv  Detail & Related papers  (2020-02-14T10:00:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.