Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

Geometric Convolutional Neural Network for Analyzing Surface-Based Neuroimaging Data

The conventional CNN, widely used for two-dimensional images, however, is not directly applicable to non-regular geometric surface, such as a cortical thickness. We propose Geometric CNN (gCNN) that deals with data representation over a spherical surface and renders pattern recognition in a multi-shell mesh structure. The classification accuracy for sex was significantly higher than that of SVM and image based CNN. It only uses MRI thickness data to classify gender but this method can expand to classify disease from other MRI or fMRI dataComment: 29 page

A Survey on Deep Learning in Medical Image Analysis

Deep learning algorithms, in particular convolutional networks, have rapidly become a methodology of choice for analyzing medical images. This paper reviews the major deep learning concepts pertinent to medical image analysis and summarizes over 300 contributions to the field, most of which appeared in the last year. We survey the use of deep learning for image classification, object detection, segmentation, registration, and other tasks and provide concise overviews of studies per application area. Open challenges and directions for future research are discussed.Comment: Revised survey includes expanded discussion section and reworked introductory section on common deep architectures. Added missed papers from before Feb 1st 201

Random fields of multivariate test statistics, with applications to shape analysis

Our data are random fields of multivariate Gaussian observations, and we fit a multivariate linear model with common design matrix at each point. We are interested in detecting those points where some of the coefficients are nonzero using classical multivariate statistics evaluated at each point. The problem is to find the $P$-value of the maximum of such a random field of test statistics. We approximate this by the expected Euler characteristic of the excursion set. Our main result is a very simple method for calculating this, which not only gives us the previous result of Cao and Worsley [Ann. Statist. 27 (1999) 925--942] for Hotelling's $T^2$, but also random fields of Roy's maximum root, maximum canonical correlations [Ann. Appl. Probab. 9 (1999) 1021--1057], multilinear forms [Ann. Statist. 29 (2001) 328--371], $\bar{\chi}^2$ [Statist. Probab. Lett 32 (1997) 367--376, Ann. Statist. 25 (1997) 2368--2387] and $\chi^2$ scale space [Adv. in Appl. Probab. 33 (2001) 773--793]. The trick involves approaching the problem from the point of view of Roy's union-intersection principle. The results are applied to a problem in shape analysis where we look for brain damage due to nonmissile trauma.Comment: Published in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Colocalization of neurons in optical coherence microscopy and Nissl-stained histology in Brodmann’s area 32 and area 21

Published in final edited form as: Brain Struct Funct. 2019 January ; 224(1): 351–362. doi:10.1007/s00429-018-1777-z.Optical coherence tomography is an optical technique that uses backscattered light to highlight intrinsic structure, and when applied to brain tissue, it can resolve cortical layers and fiber bundles. Optical coherence microscopy (OCM) is higher resolution (i.e., 1.25 µm) and is capable of detecting neurons. In a previous report, we compared the correspondence of OCM acquired imaging of neurons with traditional Nissl stained histology in entorhinal cortex layer II. In the current method-oriented study, we aimed to determine the colocalization success rate between OCM and Nissl in other brain cortical areas with different laminar arrangements and cell packing density. We focused on two additional cortical areas: medial prefrontal, pre-genual Brodmann area (BA) 32 and lateral temporal BA 21. We present the data as colocalization matrices and as quantitative percentages. The overall average colocalization in OCM compared to Nissl was 67% for BA 32 (47% for Nissl colocalization) and 60% for BA 21 (52% for Nissl colocalization), but with a large variability across cases and layers. One source of variability and confounds could be ascribed to an obscuring effect from large and dense intracortical fiber bundles. Other technical challenges, including obstacles inherent to human brain tissue, are discussed. Despite limitations, OCM is a promising semi-high throughput tool for demonstrating detail at the neuronal level, and, with further development, has distinct potential for the automatic acquisition of large databases as are required for the human brain.Accepted manuscrip

Sparse Representation-Based Framework for Preprocessing Brain MRI

This thesis addresses the use of sparse representations, specifically Dictionary Learning and Sparse Coding, for pre-processing brain MRI, so that the processed image retains the fine details of the original image, to improve the segmentation of brain structures, to assess whether there is any relationship between alterations in brain structures and the behavior of young offenders. Denoising an MRI while keeping fine details is a difficult task; however, the proposed method, based on sparse representations, NLM, and SVD can filter noise while prevents blurring, artifacts, and residual noise. Segmenting an MRI is a non-trivial task; because normally the limits between regions in these images may be neither clear nor well defined, due to the problems which affect MRI. However, this method, from both the label matrix of the segmented MRI and the original image, yields a new improved label matrix in which improves the limits among regions.DoctoradoDoctor en Ingeniería de Sistemas y Computació

Knowledge-Based Deformable Surface Model with Application to Segmentation of Brain Structures in MRI

We have developed a knowledge-based deformable surface for segmentation of medical images. This work has been done in the context of segmentation of hippocampus from brain MRI, due to its challenge and clinical importance. The model has a polyhedral discrete structure and is initialized automatically by analyzing brain MRI sliced by slice, and finding few landmark features at each slice using an expert system. The expert system decides on the presence of the hippocampus and its general location in each slice. The landmarks found are connected together by a triangulation method, to generate a closed initial surface. The surface deforms under defined internal and external force terms thereafter, to generate an accurate and reproducible boundary for the hippocampus. The anterior and posterior (AP) limits of the hippocampus is estimated by automatic analysis of the location of brain stem, and some of the features extracted in the initialization process. These data are combined together with a priori knowledge using Bayes method to estimate a probability density function (pdf) for the length of the structure in sagittal direction. The hippocampus AP limits are found by optimizing this pdf. The model is tested on real clinical data and the results show very good model performance.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85930/1/Fessler166.pd