Anisotropic nonlocal means denoising Maleki, Arian; Narayan, Manjari; Baraniuk, Richard G.
Applied and computational harmonic analysis,
November 2013, 2013-11-00, 20131101, Letnik:
35, Številka:
3
Journal Article
Recenzirano
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It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the ...neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.
Many complex brain disorders, such as autism spectrum disorders, exhibit a wide range of symptoms and disability. To understand how brain communication is impaired in such conditions, functional ...connectivity studies seek to understand individual differences in brain network structure in terms of covariates that measure symptom severity. In practice, however, functional connectivity is not observed but estimated from complex and noisy neural activity measurements. Imperfect subject network estimates can compromise subsequent efforts to detect covariate effects on network structure. We address this problem in the case of Gaussian graphical models of functional connectivity, by proposing novel two-level models that treat both subject level networks and population level covariate effects as unknown parameters. To account for imperfectly estimated subject level networks when fitting these models, we propose two related approaches-R (2) based on resampling and random effects test statistics, and R (3) that additionally employs random adaptive penalization. Simulation studies using realistic graph structures reveal that R (2) and R (3) have superior statistical power to detect covariate effects compared to existing approaches, particularly when the number of within subject observations is comparable to the size of subject networks. Using our novel models and methods to study parts of the ABIDE dataset, we find evidence of hypoconnectivity associated with symptom severity in autism spectrum disorders, in frontoparietal and limbic systems as well as in anterior and posterior cingulate cortices.
Synesthesia is a condition in which normal stimuli can trigger anomalous associations. In this study, we exploit synesthesia to understand how the synesthetic experience can be explained by subtle ...changes in network properties. Of the many forms of synesthesia, we focus on colored sequence synesthesia, a form in which colors are associated with overlearned sequences, such as numbers and letters (graphemes). Previous studies have characterized synesthesia using resting-state connectivity or stimulus-driven analyses, but it remains unclear how network properties change as synesthetes move from one condition to another. To address this gap, we used functional MRI in humans to identify grapheme-specific brain regions, thereby constructing a functional "synesthetic" network. We then explored functional connectivity of color and grapheme regions during a synesthesia-inducing fMRI paradigm involving rest, auditory grapheme stimulation, and audiovisual grapheme stimulation. Using Markov networks to represent direct relationships between regions, we found that synesthetes had more connections during rest and auditory conditions. We then expanded the network space to include 90 anatomical regions, revealing that synesthetes tightly cluster in visual regions, whereas controls cluster in parietal and frontal regions. Together, these results suggest that synesthetes have increased connectivity between grapheme and color regions, and that synesthetes use visual regions to a greater extent than controls when presented with dynamic grapheme stimulation. These data suggest that synesthesia is better characterized by studying global network dynamics than by individual properties of a single brain region.
We conduct an asymptotic risk analysis of the nonlocal means image denoising algorithm for the Horizon class of images that are piecewise constant with a sharp edge discontinuity. We prove that the ...mean square risk of an optimally tuned nonlocal means algorithm decays according to n−1log1/2+ϵn, for an n×n-pixel image with ϵ>0. This decay rate is an improvement over some of the predecessors of this algorithm, including the linear convolution filter, median filter, and the SUSAN filter, each of which provides a rate of only n−2/3. It is also within a logarithmic factor from optimally tuned wavelet thresholding. However, it is still substantially lower than the optimal minimax rate of n−4/3.
Groupyr: Sparse Group Lasso in Python Richie-Halford, Adam; Narayan, Manjari; Simon, Noah ...
Journal of open source software,
01/2021, Letnik:
6, Številka:
58
Journal Article
Odprti dostop
For high-dimensional supervised learning, it is often beneficial to use domain-specific knowledge to improve the performance of statistical learning models. When the problem contains covariates which ...form groups, researchers can include this grouping information to find parsimonious representations of the relationship between covariates and targets. These groups may arise artificially, as from the polynomial expansion of a smaller feature space, or naturally, as from the anatomical grouping of different brain regions or the geographical grouping of different cities. When the number of features is large compared to the number of observations, one seeks a subset of the features which is sparse at both the group and global level.
In many neuroimaging modalities, scientists observe neural activity at distinct units of brain function but seek to study and manipulate functional connectivity or unobserved latent relationships ...between these units. Functional connectivity is commonly described using networks where nodes correspond to brain locations or regions, electrodes, circuits or neurons while edges correspond to some notion of statistical dependence. Such net- work models are increasingly used in clinical neuroimaging where scientists seek to find robust network biomarkers to detect specific brain based disorders, explain underlying disease mechanisms and guide personalized treatment regimes. However, functional con- nectivity networks are never observed but estimated from complex and noisy data, and as a result, estimated networks are prone to statistical errors. This dissertation shows that failure to account for such statistical errors compromises subsequent inferential analyses to find differences in functional connectivity and proposes a new statistical framework that ameliorates these problems, thus improving the reproducibility of functional connectivity studies. Formally, this dissertation identifies a new statistical problem, Population Post-Selection Inference or popPSI, that arises in functional neuroimaging when scientists ask inferential questions such as — How do network metrics differ between a population of unhealthy subjects and healthy controls How do individual networks vary with symptom severity To investigate popPSI issues in such questions, we use two level models to study network differences, specifically employing Gaussian graphical models (GGMs) for functional connectivity. Whereas standard test statistics do not adequately control type I and type II errors for such models, R3, our novel methodological approach, based on resampling, random penalization with random effects test statistics addresses the deficiencies of current test statistics employed in neuroimaging. Our framework is general and can be used to test general linear hypotheses of the network at the edge, node or global level. Using extensive simulation studies for a wide variety of sample sizes and network structures, we show that R3 offers improvements in statistical power and error for various network met- rics. Real data case studies reveal that our methods find meaningful and clinically relevant network differences in synesthesia, neurofibromatosis-1 and autism spectrum disorders.
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