Non-Gaussianity analysis on local morphological measures of WMAP data

The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity, and elongation of the signal's local features. In the present work, the non-Gaussianity of the WMAP temperature data of the cosmic microwave background (CMB) is analyzed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcminutes and 30 degrees on the celestial sphere. While no detection is made neither in the orientation analysis nor in the elongation analysis, a strong detection is made in the excess kurtosis of the signed-intensity of the WMAP data. The non-Gaussianity is observed with a significance level below 0.5% at a wavelet scale corresponding to an angular size around 10 degrees, and confirmed at neighbour scales. This supports a previous detection of an excess of kurtosis in the wavelet coefficient of the WMAP data with the axisymmetric Mexican hat wavelet (Vielva et al. 2004). Instrumental noise and foreground emissions are not likely to be at the origin of the excess of kurtosis. Large-scale modulations of the CMB related to some unknown systematics are rejected as possible origins of the detection. The observed non-Gaussianity may therefore probably be imputed to the CMB itself, thereby questioning the basic inflationary scenario upon which the present concordance cosmological model relies. Taking the CMB temperature angular power spectrum of the concordance cosmological model at face value, further analysis also suggests that this non-Gaussianity is not confined to the directions on the celestial sphere with an anomalous signed-intensity.Comment: 10 pages, 3 figures. Version 2 includes minor changes to match version accepted for publication in MNRA

A control algorithm for autonomous optimization of extracellular recordings

This paper develops a control algorithm that can autonomously position an electrode so as to find and then maintain an optimal extracellular recording position. The algorithm was developed and tested in a two-neuron computational model representative of the cells found in cerebral cortex. The algorithm is based on a stochastic optimization of a suitably defined signal quality metric and is shown capable of finding the optimal recording position along representative sampling directions, as well as maintaining the optimal signal quality in the face of modeled tissue movements. The application of the algorithm to acute neurophysiological recording experiments and its potential implications to chronic recording electrode arrays are discussed

The Incremental Multiresolution Matrix Factorization Algorithm

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric matrices -- an important aspect in the success of many vision problems. Our new algorithm, the incremental multiresolution matrix factorization, uncovers such structure one feature at a time, and hence scales well to large matrices. We describe how this multiscale analysis goes much farther than what a direct global factorization of the data can identify. We evaluate the efficacy of the resulting factorizations for relative leveraging within regression tasks using medical imaging data. We also use the factorization on representations learned by popular deep networks, providing evidence of their ability to infer semantic relationships even when they are not explicitly trained to do so. We show that this algorithm can be used as an exploratory tool to improve the network architecture, and within numerous other settings in vision.Comment: Computer Vision and Pattern Recognition (CVPR) 2017, 10 page

Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data

Image data are increasingly encountered and are of growing importance in many areas of science. Much of these data are quantitative image data, which are characterized by intensities that represent some measurement of interest in the scanned images. The data typically consist of multiple images on the same domain and the goal of the research is to combine the quantitative information across images to make inference about populations or interventions. In this paper we present a unified analysis framework for the analysis of quantitative image data using a Bayesian functional mixed model approach. This framework is flexible enough to handle complex, irregular images with many local features, and can model the simultaneous effects of multiple factors on the image intensities and account for the correlation between images induced by the design. We introduce a general isomorphic modeling approach to fitting the functional mixed model, of which the wavelet-based functional mixed model is one special case. With suitable modeling choices, this approach leads to efficient calculations and can result in flexible modeling and adaptive smoothing of the salient features in the data. The proposed method has the following advantages: it can be run automatically, it produces inferential plots indicating which regions of the image are associated with each factor, it simultaneously considers the practical and statistical significance of findings, and it controls the false discovery rate.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS407 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org