Sparse topological data recovery in medical images

Abstract

For medical image analysis, the test statistic of the measurements is usually constructed at every voxels in space and thresholded to determine the regions of significant signals. This thresholding produces a small patch of regions around the critical values of the test statistic. It is known that the probability of the critical values bigger than a specific threshold can be computed as the expectation of the Euler characteristic of the patch. Motivated by this topological connection, we present a new computational framework of modeling various functional measurements as topological objects.The level set associated with functional measurements can be approximated using a simplicial complex consisting of nodes and links. The existence of links basically determine the underlying topological structure of the signal. The strength of links can be modeled using an underdetermined linear model. By incorporating sparsity into the model, the links can be sparsely obtained making interpretation and visualization of the simplicial complex easier. The main contribution of this paper is showing the relationship between sparse topological structures to the sparse regression framework. We apply this novel framework in constructing a structural brain network model.

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the L 2,1 Norms and Affine Transformation

“…Robust methods are the fundamental methods for image alignment and reconstruction [1,2], video surveillance, text, video, and bioinformatics. Such approach is important to get the true underlying objects in highly correlated and complex high-dimensional images in which the approaches are applied in various applications in the areas of signal processing, images, texts, videos, and bioinformatics [3][4][5][6][7][8]. Moreover, this problem faces some severe challenges due to various annoying e ects.…”

Classification of multiple sclerosis lesions using adaptive dictionary learning

“…Recent publications have demonstrated the effectiveness of sparse representation techniques in medical applications such as shape modelling [10], constructing a structural http://dx.doi.org/10.1016/j.compmedimag.2015.05.003 0895-6111/© 2015 Elsevier Ltd. All rights reserved. brain network model [11] and predicting cognitive data from medical images [12]. In addition, the dictionary learning framework has been used in deformable segmentation [13], image fusion [14], super-resolution analysis [15], denoising [16,17], deconvolution of low-dose computed tomography perfusion [18,19] and low-dose blood-brain barrier permeability quantification [20].…”