Spectral Decomposition of Discrepancy Kernels on the Euclidean Ball, the Special Orthogonal Group, and the Grassmannian Manifold.

To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of Rd. For restrictions to the Euclidean ball in odd dimensions, to the rotation group SO(3), and to the Grassmannian manifold G2,4, we compute the kernels' Fourier coefficients and determine their asymptotics. The L2-discrepancy is then expressed in the Fourier domain that enables efficient numerical minimization based on the nonequispaced fast Fourier transform. For SO(3), the nonequispaced fast Fourier transform is publicly available, and, for G2,4, the transform is derived here. We also provide numerical experiments for SO(3) and G2,4.

RedundancyMiner: De-replication of redundant GO categories in microarray and proteomics analysis.

BACKGROUND: The Gene Ontology (GO) Consortium organizes genes into hierarchical categories based on biological process, molecular function and subcellular localization. Tools such as GoMiner can leverage GO to perform ontological analysis of microarray and proteomics studies, typically generating a list of significant functional categories. Two or more of the categories are often redundant, in the sense that identical or nearly-identical sets of genes map to the categories. The redundancy might typically inflate the report of significant categories by a factor of three-fold, create an illusion of an overly long list of significant categories, and obscure the relevant biological interpretation. RESULTS: We now introduce a new resource, RedundancyMiner, that de-replicates the redundant and nearly-redundant GO categories that had been determined by first running GoMiner. The main algorithm of RedundancyMiner, MultiClust, performs a novel form of cluster analysis in which a GO category might belong to several category clusters. Each category cluster follows a "complete linkage" paradigm. The metric is a similarity measure that captures the overlap in gene mapping between pairs of categories. CONCLUSIONS: RedundancyMiner effectively eliminated redundancies from a set of GO categories. For illustration, we have applied it to the clarification of the results arising from two current studies: (1) assessment of the gene expression profiles obtained by laser capture microdissection (LCM) of serial cryosections of the retina at the site of final optic fissure closure in the mouse embryos at specific embryonic stages, and (2) analysis of a conceptual data set obtained by examining a list of genes deemed to be "kinetochore" genes.

Automated Quantification of Photoreceptor alteration in macular disease using Optical Coherence Tomography and Deep Learning.

Diabetic macular edema (DME) and retina vein occlusion (RVO) are macular diseases in which central photoreceptors are affected due to pathological accumulation of fluid. Optical coherence tomography allows to visually assess and evaluate photoreceptor integrity, whose alteration has been observed as an important biomarker of both diseases. However, the manual quantification of this layered structure is challenging, tedious and time-consuming. In this paper we introduce a deep learning approach for automatically segmenting and characterising photoreceptor alteration. The photoreceptor layer is segmented using an ensemble of four different convolutional neural networks. En-face representations of the layer thickness are produced to characterize the photoreceptors. The pixel-wise standard deviation of the score maps produced by the individual models is also taken to indicate areas of photoreceptor abnormality or ambiguous results. Experimental results showed that our ensemble is able to produce results in pair with a human expert, outperforming each of its constitutive models. No statistically significant differences were observed between mean thickness estimates obtained from automated and manually generated annotations. Therefore, our model is able to reliable quantify photoreceptors, which can be used to improve prognosis and managment of macular diseases.

Modeling Photo-Bleaching Kinetics to Create High Resolution Maps of Rod Rhodopsin in the Human Retina.

We introduce and describe a novel non-invasive in-vivo method for mapping local rod rhodopsin distribution in the human retina over a 30-degree field. Our approach is based on analyzing the brightening of detected lipofuscin autofluorescence within small pixel clusters in registered imaging sequences taken with a commercial 488nm confocal scanning laser ophthalmoscope (cSLO) over a 1 minute period. We modeled the kinetics of rhodopsin bleaching by applying variational optimization techniques from applied mathematics. The physical model and the numerical analysis with its implementation are outlined in detail. This new technique enables the creation of spatial maps of the retinal rhodopsin and retinal pigment epithelium (RPE) bisretinoid distribution with an ≈ 50µm resolution.

Modifications of iterative schemes used for curvature correction in noninvasive biomedical imaging.

Iterative polynomial fitting along image rows and columns has recently been used to remove curvature bias in multispectral image sets of the human forearm and phantoms. However, this method is only applicable if foreground and background features satisfy strong separation conditions. In this method, we verify that the iterative polynomial approach converges toward bivariate polynomial fitting, and, hence, the resulting fit corresponds to low-pass filtering the image. In contrast to the iterative fitting, the bivariate polynomial fit can be performed on images with missing or excluded parts. Indeed, our observation enables us to modify the scheme and significantly weaken the required assumptions on foreground/background separation allowing a wider range of application.

Schroedinger Eigenmaps for the analysis of biomedical data.

We introduce Schroedinger Eigenmaps (SE), a new semi-supervised manifold learning and recovery technique. This method is based on an implementation of graph Schroedinger operators with appropriately constructed barrier potentials as carriers of labeled information. We use our approach for the analysis of standard biomedical datasets and new multispectral retinal images.

Nonlinear gene cluster analysis with labeling for microarray gene expression data in organ development.

BACKGROUND: The gene networks underlying closure of the optic fissure during vertebrate eye development are not well-understood. We use a novel clustering method based on nonlinear dimension reduction with data labeling to analyze microarray data from laser capture microdissected (LCM) cells at the site and developmental stages (days 10.5 to 12.5) of optic fissure closure. RESULTS: Our nonlinear methods created clusters of genes that mapped onto more specific biological processes and functions related to eye development as defined by Gene Ontology at lower false discovery rates than conventional linear cluster algorithms. Our new methods build on the advantages of LCM to isolate pure phenotypic populations within complex tissues in order to identify systems biology relationships among critical gene products expressed at lower copy number. CONCLUSIONS: The combination of LCM of embryonic organs, gene expression microarrays, and nonlinear dimension reduction with labeling is a potentially useful approach to extract subtle spatial and temporal co-variations within the gene regulatory networks that specify mammalian organogenesis and organ function. Our results motivate further analysis of nonlinear dimension reduction with labeling within other microarray data sets from LCM dissected tissues or other cell specific samples to determine the more general utility of our method for uncovering more specific biological functional relationships.

Quantitative principal component model for skin chromophore mapping using multi-spectral images and spatial priors.

We describe a novel reconstruction algorithm based on Principal Component Analysis (PCA) applied to multi-spectral imaging data. Using numerical phantoms, based on a two layered skin model developed previously, we found analytical expressions, which convert qualitative PCA results into quantitative blood volume and oxygenation values, assuming the epidermal thickness to be known. We also evaluate the limits of accuracy of this method when the value of the epidermal thickness is not known. We show that blood volume can reliably be extracted (less than 6% error) even if the assumed thickness deviates 0.04mm from the actual value, whereas the error in blood oxygenation can be as large as 25% for the same deviation in thickness. This PCA based reconstruction was found to extract blood volume and blood oxygenation with less than 8% error, if the underlying structure is known. We then apply the method to in vivo multi-spectral images from a healthy volunteer's lower forearm, complemented by images of the same area using Optical Coherence Tomography (OCT) for measuring the epidermal thickness. Reconstruction of the imaging results using a two layered analytical skin model was compared to PCA based reconstruction results. A point wise correlation was found, showing the proof of principle of using PCA based reconstruction for blood volume and oxygenation extraction.

Principal component model of multispectral data for near real-time skin chromophore mapping.

Multispectral images of skin contain information on the spatial distribution of biological chromophores, such as blood and melanin. From this, parameters such as blood volume and blood oxygenation can be retrieved using reconstruction algorithms. Most such approaches use some form of pixelwise or volumetric reconstruction code. We explore the use of principal component analysis (PCA) of multispectral images to access blood volume and blood oxygenation in near real time. We present data from healthy volunteers under arterial occlusion of the forearm, experiencing ischemia and reactive hyperemia. Using a two-layered analytical skin model, we show reconstruction results of blood volume and oxygenation and compare it to the results obtained from our new spectral analysis based on PCA. We demonstrate that PCA applied to multispectral images gives near equivalent results for skin chromophore mapping and quantification with the advantage of being three orders of magnitude faster than the reconstruction algorithm.

Direct curvature correction for noncontact imaging modalities applied to multispectral imaging.

Noncontact optical imaging of curved objects can result in strong artifacts due to the object's shape, leading to curvature biased intensity distributions. This artifact can mask variations due to the object's optical properties, and makes reconstruction of optical/physiological properties difficult. In this work we demonstrate a curvature correction method that removes this artifact and recovers the underlying data, without the necessity of measuring the object's shape. This method is applicable to many optical imaging modalities that suffer from shape-based intensity biases. By separating the spatially varying data (e.g., physiological changes) from the background signal (dc component), we show that the curvature can be extracted by either averaging or fitting the rows and columns of the images. Numerical simulations show that our method is equivalent to directly removing the curvature, when the object's shape is known, and accurately recovers the underlying data. Experiments on phantoms validate the numerical results and show that for a given image with 16.5% error due to curvature, the method reduces that error to 1.2%. Finally, diffuse multispectral images are acquired on forearms in vivo. We demonstrate the enhancement in image quality on intensity images, and consequently on reconstruction results of blood volume and oxygenation distributions.