Image patch analysis of sunspots and active regions. I. Intrinsic dimension and correlation analysis

The flare-productivity of an active region is observed to be related to its spatial complexity. Mount Wilson or McIntosh sunspot classifications measure such complexity but in a categorical way, and may therefore not use all the information present in the observations. Moreover, such categorical schemes hinder a systematic study of an active region's evolution for example. We propose fine-scale quantitative descriptors for an active region's complexity and relate them to the Mount Wilson classification. We analyze the local correlation structure within continuum and magnetogram data, as well as the cross-correlation between continuum and magnetogram data. We compute the intrinsic dimension, partial correlation, and canonical correlation analysis (CCA) of image patches of continuum and magnetogram active region images taken from the SOHO-MDI instrument. We use masks of sunspots derived from continuum as well as larger masks of magnetic active regions derived from the magnetogram to analyze separately the core part of an active region from its surrounding part. We find the relationship between complexity of an active region as measured by Mount Wilson and the intrinsic dimension of its image patches. Partial correlation patterns exhibit approximately a third-order Markov structure. CCA reveals different patterns of correlation between continuum and magnetogram within the sunspots and in the region surrounding the sunspots. These results also pave the way for patch-based dictionary learning with a view towards automatic clustering of active regions.Comment: Accepted for publication in the Journal of Space Weather and Space Climate (SWSC). 23 pages, 11 figure

Tensor Regression with Applications in Neuroimaging Data Analysis

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.Comment: 27 pages, 4 figure

Learning midlevel image features for natural scene and texture classification

This paper deals with coding of natural scenes in order to extract semantic information. We present a new scheme to project natural scenes onto a basis in which each dimension encodes statistically independent information. Basis extraction is performed by independent component analysis (ICA) applied to image patches culled from natural scenes. The study of the resulting coding units (coding filters) extracted from well-chosen categories of images shows that they adapt and respond selectively to discriminant features in natural scenes. Given this basis, we define global and local image signatures relying on the maximal activity of filters on the input image. Locally, the construction of the signature takes into account the spatial distribution of the maximal responses within the image. We propose a criterion to reduce the size of the space of representation for faster computation. The proposed approach is tested in the context of texture classification (111 classes), as well as natural scenes classification (11 categories, 2037 images). Using a common protocol, the other commonly used descriptors have at most 47.7% accuracy on average while our method obtains performances of up to 63.8%. We show that this advantage does not depend on the size of the signature and demonstrate the efficiency of the proposed criterion to select ICA filters and reduce the dimensio

Statistical Compressed Sensing of Gaussian Mixture Models

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is introduced. SCS based on Gaussian models is investigated in depth. For signals that follow a single Gaussian model, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS based on sparse models, where N is the signal dimension, and with an optimal decoder implemented via linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the best k-term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional sparsity-oriented CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is upper bounded by a constant times the best k-term approximation with probability one, and the bound constant can be efficiently calculated. For Gaussian mixture models (GMMs), that assume multiple Gaussian distributions and that each signal follows one of them with an unknown index, a piecewise linear estimator is introduced to decode SCS. The accuracy of model selection, at the heart of the piecewise linear decoder, is analyzed in terms of the properties of the Gaussian distributions and the number of sensing measurements. A maximum a posteriori expectation-maximization algorithm that iteratively estimates the Gaussian models parameters, the signals model selection, and decodes the signals, is presented for GMM-based SCS. In real image sensing applications, GMM-based SCS is shown to lead to improved results compared to conventional CS, at a considerably lower computational cost