Statistical Inference Models for Image Datasets with Systematic Variations

Associations Between Positron Emission Tomography Amyloid Pathology and Diffusion Tensor Imaging Brain Connectivity in Pre-Clinical Alzheimer's Disease

Characterizing Alzheimer's disease (AD) at pre-clinical stages is crucial for initiating early treatment strategies. It is widely accepted that amyloid accumulation is a primary pathological event in AD. Also, loss of connectivity between brain regions is suspected of contributing to cognitive decline, but studies that test these associations using either local (i.e., individual edges) or global (i.e., modularity) connectivity measures may be limited. In this study, we utilized data acquired from 139 cognitively unimpaired participants. Sixteen gray matter (GM) regions known to be affected by AD were selected for analysis. For each of the 16 regions, the effect of amyloid burden, measured using Pittsburgh Compound B (PiB) positron emission tomography, on each of the 1761 brain network connections derived from diffusion tensor imaging (DTI) connecting 162 GM regions, was investigated. Applying our unique multiresolution statistical analysis called the Wavelet Connectivity Signature (WaCS), this study demonstrates the relationship between amyloid burden and structural brain connectivity as assessed with DTI. Our statistical analysis using WaCS shows that in 15 of 16 GM regions, statistically significant relationships between amyloid burden in those regions and structural connectivity networks were observed. After applying multiple testing correction, 10 unique structural brain connections were found to be significantly associated with amyloid accumulation. For 7 of those 10 network connections, the decrease in their network connection strength indexed by fractional anisotropy was, in turn, associated with lower cognitive function, providing evidence that AD-related structural connectivity loss is a correlate of cognitive decline.

Online Graph Completion: Multivariate Signal Recovery in Computer Vision

The adoption of "human-in-the-loop" paradigms in computer vision and machine learning is leading to various applications where the actual data acquisition (e.g., human supervision) and the underlying inference algorithms are closely interwined. While classical work in active learning provides effective solutions when the learning module involves classification and regression tasks, many practical issues such as partially observed measurements, financial constraints and even additional distributional or structural aspects of the data typically fall outside the scope of this treatment. For instance, with sequential acquisition of partial measurements of data that manifest as a matrix (or tensor), novel strategies for completion (or collaborative filtering) of the remaining entries have only been studied recently. Motivated by vision problems where we seek to annotate a large dataset of images via a crowdsourced platform or alternatively, complement results from a state-of-the-art object detector using human feedback, we study the "completion" problem defined on graphs, where requests for additional measurements must be made sequentially. We design the optimization model in the Fourier domain of the graph describing how ideas based on adaptive submodularity provide algorithms that work well in practice. On a large set of images collected from Imgur, we see promising results on images that are otherwise difficult to categorize. We also show applications to an experimental design problem in neuroimaging.

On Statistical Analysis of Neuroimages with Imperfect Registration

A variety of studies in neuroscience/neuroimaging seek to perform statistical inference on the acquired brain image scans for diagnosis as well as understanding the pathological manifestation of diseases. To do so, an important first step is to register (or co-register) all of the image data into a common coordinate system. This permits meaningful comparison of the intensities at each voxel across groups (e.g., diseased versus healthy) to evaluate the effects of the disease and/or use machine learning algorithms in a subsequent step. But errors in the underlying registration make this problematic, they either decrease the statistical power or make the follow-up inference tasks less effective/accurate. In this paper, we derive a novel algorithm which offers immunity to local errors in the underlying deformation field obtained from registration procedures. By deriving a deformation invariant representation of the image, the downstream analysis can be made more robust as if one had access to a (hypothetical) far superior registration procedure. Our algorithm is based on recent work on scattering transform. Using this as a starting point, we show how results from harmonic analysis (especially, non-Euclidean wavelets) yields strategies for designing deformation and additive noise invariant representations of large 3-D brain image volumes. We present a set of results on synthetic and real brain images where we achieve robust statistical analysis even in the presence of substantial deformation errors; here, standard analysis procedures significantly under-perform and fail to identify the true signal.