Robust neural network for wavefront reconstruction using Zernike coefficients

Accurately measuring optical aberrations is an important process for several eyecare tasks. Managing the individual variations found in human eyes plays a large role in properly defining these aberrations. A common method to measure optical aberrations uses sensors to locally capture the gradients across a grid of points. This data is used to reconstruct the wavefront resulting from light passing through the eye. In using this method of measurement, typical individual variations such as scarring or eyelashes can lead to shortcomings in the data. These shortcomings can manifest as noise or even areas of entirely missing data. The use of ANN (artificial neural networks) is one way to minimize the effects of these unpredictable deviations.

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The Resolution Matrix for Visualizing Functional Network Connectivity

The resolution matrix is a mathematical tool for analyzing inverse problems such as computational imaging systems. When treating network connectivity estimation as an inverse problem, the resolution matrix describes the degree to which network nodes and edges can be resolved. This is useful both for quantifying robustness of the network estimate, as well as identifying correlated activity. In this report we analyze the resolution matrix for functional MRI data from the Human Connectome project. We find that common metrics of the resolution metric can be used to identify networked activity, though with a new twist on the relationship between default mode network and the frontoparietal attention network.

https://arxiv.org/abs/2009.03187 (pdf).

Resolution-based spectral clustering for brain parcellation using functional MRI

Brain parcellation is important for exploiting neuroimaging data. Variability in physiology between individuals has led to the need for data-driven approaches to parcellation, with recent research focusing on simultaneously estimating and partitioning the network structure of the brain. We view data preprocessing, parcellation, and parcel validation from the perspective of predictive modeling. The goal is to identify parcels in a way that best generalizes to unseen data. We utilize an uncertainty quantification approach from image science to define parcels as groups of unresolvable variables in the predictive model.

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Feature-level Malware Obfuscation in Deep Learning

We consider the problem of detecting malware with deep learning models, where the malware may be combined with significant amounts of benign code. Examples of this include piggybacking and trojan horse attacks on a system, where malicious behavior is hidden within a useful application. Such added flexibility in augmenting the malware enables significantly more code obfuscation. Hence we focus on the use of static features, particularly Intents, Permissions, and API calls, which we presume cannot be ultimately hidden from the Android system, but only augmented with yet more such features. We first train a deep neural network classifier for malware classification using features of benign and malware samples. Then we demonstrate a steep increase in false negative rate (ie, attacks succeed), simply by randomly adding features of a benign app to malware. Finally we test the use of data augmentation to harden the classifier against such attacks. We find that for API calls, it is possible to reject the vast majority of attacks, where using Intents or Permissions is less successful.

https://arxiv.org/pdf/2002.05517

Quadratic Programming with Keras

This note describes how to implement and solve a quadratic programming optimization problem using a shallow neural network in Keras. A single linear layer is used with a custom one-sided loss to impose the inequality constraints. A custom kernel regularizer is used to impose the optimization objective, yielding a form of penalty method. This provides a useful exercise in augmenting the loss, metrics, and callbacks used in Keras. This also potentially allows the exploitation of the back-end implementations of Keras and Tensorflow on GPU’s and distributed storage. We demonstrate the method for large-scale computational image reconstruction with compressed sensing simulations.

www.keithdillon.com/papers_preprints/Quadratic Programming with Keras.pdf

Clustering Gaussian Graphical Models

We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial correlations. In the limited-data scenario, where the covariance matrix would be rank-deficient, we are able to make use of matrix factors, and never need to estimate the actual covariance or precision matrix. We demonstrate the method on functional MRI data from the Human Connectome Project. A matlab implementation of the algorithm is provided.

https://arxiv.org/pdf/1910.02342

For Matlab code, read ‘more’

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On the Computation and Applications of Large Dense Partial Correlation Networks

While sparse inverse covariance matrices are very popular for modeling network connectivity, the value of the dense solution is often overlooked. In fact the L2-regularized solution has deep connections to a number of important applications to spectral graph theory, dimensionality reduction, and uncertainty quantification. We derive an approach to directly compute the partial correlations based on concepts from inverse problem theory. This approach also leads to new insights on open problems such as model selection and data preprocessing, as well as new approaches which relate the above application areas.

https://arxiv.org/pdf/1903.07181

Spectral Resolution Clustering for Brain Parcellation

We take an image science perspective on the problem of determining brain network connectivity given functional activity. But adapting the concept of image resolution to this problem, we provide a new perspective on network partitioning for individual brain parcellation. The typical goal here is to determine densely-interconnected subnetworks within a larger network by choosing the best edges to cut. We instead define these subnetworks as resolution cells, where highly-correlated activity within the cells makes edge weights difficult to determine from the data. Subdividing the resolution estimates into disjoint resolution cells via clustering yields a new variation, and new perspective, on spectral clustering. This provides insight and strategies for open questions such as the selection of model order and the optimal choice of preprocessing steps for functional imaging data. The approach is demonstrated using functional imaging data, where we find the proposed approach produces parcellations which are more predictive across multiple scans versus conventional methods, as well as versus alternative forms of spectral clustering.

https://arxiv.org/pdf/1810.04026

A regularized clustering approach to brain parcellation from functional MRI data

We consider a data-driven approach for the subdivision of an individual subject’s functional Magnetic Resonance Imaging (fMRI) scan into regions of interest, i.e., brain parcellation. The approach is based on a computational technique for calculating resolution from inverse problem theory, which we apply to neighborhood selection for brain connectivity networks. This can be efficiently calculated even for very large images, and explicitly incorporates regularization in the form of spatial smoothing and a noise cutoff. We demonstrate the reproducibility of the method on multiple scans of the same subjects, as well as the variations between subjects.

Keith Dillon, Yu-Ping Wang, ” A regularized clustering approach to brain parcellation from functional MRI data“, Proc. SPIE 10394, Wavelets and Sparsity XVII, 103940E (2017/08/24); doi: 10.1117/12.2274846; http://dx.doi.org/10.1117/12.2274846