Recently graph theory and complex networks have been widely used as a mean to model functionality of the brain. Among different neuroimaging techniques available for constructing the brain functional networks, electroencephalography (EEG) with its high temporal resolution is a useful instrument of the analysis of functional interdependencies between different brain regions. Alzheimer's disease (AD) is a neurodegenerative disease, which leads to substantial cognitive decline, and eventually, dementia in aged people. To achieve a deeper insight into the behavior of functional cerebral networks in AD, here we study their synchronizability in 17 newly diagnosed AD patients compared to 17 healthy control subjects at no-task, eyes-closed condition. The cross-correlation of artifact-free EEGs was used to construct brain functional networks. The extracted networks were then tested for their synchronization properties by calculating the eigenratio of the Laplacian matrix of the connection graph, i.e., the largest eigenvalue divided by the second smallest one. In AD patients, we found an increase in the eigenratio, i.e., a decrease in the synchronizability of brain networks across delta, alpha, beta, and gamma EEG frequencies within the wide range of network costs. The finding indicates the destruction of functional brain networks in early AD.

In PET image reconstruction, regularization is often needed to reduce the noise in the resulting images. Patch-based image processing techniques have recently been successfully used for regularization in medical image reconstruction through a penalized likelihood framework. Re-parameterization within reconstruction is another powerful regularization technique in which the object in the scanner is re-parameterized using coefficients for spatially-extensive basis vectors. In this work, a method for extracting patch-based basis vectors from the subject's MR image is proposed. The coefficients for these basis vectors are then estimated using the conventional MLEM algorithm. Furthermore, using the alternating direction method of multipliers, an algorithm for optimizing the Poisson log-likelihood while imposing sparsity on the parameters is also proposed. This novel method is then utilized to find sparse coefficients for the patch-based basis vectors extracted from the MR image. The results indicate the superiority of the proposed methods to patch-based regularization using the penalized likelihood framework.

Modern Convolutional Neural Network (CNN) architectures, despite their superiority in solving various problems, are generally too large to be deployed on resource constrained edge devices. In this paper, we reduce memory usage and floating-point operations required by convolutional layers in CNNs. We compress these layers by generalizing the Kronecker Product Decomposition to apply to multidimensional tensors, leading to the Generalized Kronecker Product Decomposition (GKPD). Our approach yields a plug-and-play module that can be used as a drop-in replacement for any convolutional layer. Experimental results for image classification on CIFAR-10 and ImageNet datasets using ResNet, MobileNetv2 and SeNet architectures substantiate the effectiveness of our proposed approach. We find that GKPD outperforms state-of-the-art decomposition methods including Tensor-Train and Tensor-Ring as well as other relevant compression methods such as pruning and knowledge distillation.

Purpose Post‐reconstruction positron emission tomography (PET) image restoration methods that take advantage of available anatomical information can play an important role in accurate quantification of PET images. However, when using anatomical information, the resulting PET image may lose resolution in certain regions where the anatomy does not agree with the change in functional activity. In this work, this problem is addressed by using both magnetic resonance (MR) and filtered PET images to guide the denoising process. Methods In this work, two novel post‐reconstruction methods for restoring PET images using the subject’s registered T1‐weighted MR image are proposed. The first method is based on a representation of the image using basis functions extracted from T1‐weighted MR and filtered PET image. The coefficients for these basis functions are estimated using a sparsity‐penalized least squares objective function. The second method is a noniterative fast method that uses guided kernel filtering in combination with twicing to restore the noisy PET image. When applied after conventional PVE correction, these methods can be considered as voxel‐based MR‐guided partial volume effect (PVE) correction methods. Results Using simulation analyses of [18F]FDG PET images of the brain with lesions, the proposed methods are compared to other denoising methods through different figures of merit. The results show promising improvements in image quality as well as reduction in bias and variance of the lesions. We also show the application of the proposed methods on real [18F]FDG data. Conclusion Two methods for restoring PET images were proposed. The methods were evaluated on simulation and real brain images. Most MR‐guided PVE correction methods are only based on segmented T1‐weighted images and their accuracy is very sensitive to segmentation errors, especially in regions of abnormalities and lesions. However, both proposed methods can use the T1‐weighted image without segmentation. The simplicity and the very low computational cost of the second method make it suitable for clinical applications and large data studies. The proposed methods can be naturally extended to PVE correction and denoising of other functional modalities using corresponding anatomical information.