Sparse And Low Rank Decomposition Based Batch Image Alignment for Speckle Reduction of retinal OCT Images

Optical Coherence Tomography (OCT) is an emerging technique in the field of biomedical imaging, with applications in ophthalmology, dermatology, coronary imaging etc. Due to the underlying physics, OCT images usually suffer from a granular pattern, called speckle noise, which restricts the process of interpretation. Here, a sparse and low rank decomposition based method is used for speckle reduction in retinal OCT images. This technique works on input data that consists of several B-scans of the same location. The next step is the batch alignment of the images using a sparse and low-rank decomposition based technique. Finally the denoised image is created by median filtering of the low-rank component of the processed data. Simultaneous decomposition and alignment of the images result in better performance in comparison to simple registration-based methods that are used in the literature for noise reduction of OCT images.Comment: Accepted for presentation at ISBI'1

Model Based Sparse Feature Extraction for Biomedical Signal Classification

This article focuses on model based sparse feature extraction of biomedical signals for classification problems, which stems from sparse representation in modern signal processing. In the presented work, a novel approach based on sparse principal component analysis (SPCA) is proposed to extract signal features. This method involves partitioning signals and utilizing SPCA to select only a limited number of signal segments in order to construct signal principal components during the training stage. For signal classification purposes, a set of regression models based on sparse principal components of the selected training signal segments is constructed. Within this approach, model residuals are estimated and used as signal features for classification. The applications of the proposed approach are demonstrated by using both the synthetic data and real EEG signals. The high classification accuracy results suggest that the proposed methods may be useful for automatic event detection using long-term observational signals. keywords: Sparse Principal Component Analysis, Sparse Feature Extraction, Signal Classification, Long-term Signal

Statistical methods for sparse functional object data: elastic curves, shapes and densities

Many applications naturally yield data that can be viewed as elements in non-linear spaces. Consequently, there is a need for non-standard statistical methods capable of handling such data. The work presented here deals with the analysis of data in complex spaces derived from functional L2-spaces as quotient spaces (or subsets of such spaces). These data types include elastic curves represented as d-dimensional functions modulo re-parametrization, planar shapes represented as 2-dimensional functions modulo rotation, scaling and translation, and elastic planar shapes combining all of these invariances. Moreover, also probability densities can be thought of as non-negative functions modulo scaling. Since these functional object data spaces lack a natural Hilbert space structure, this work proposes specialized methods that integrate techniques from functional data analysis with those for metric and manifold data. In particular, but not exclusively, novel regression methods for specific metric quotient spaces are discussed. Special attention is given to handling discrete observations, since in practice curves and shapes are typically observed only as a discrete (often sparse or irregular) set of points. Similarly, density functions are usually not directly observed, but a (small) sample from the corresponding probability distribution is available. Overall, this work comprises six contributions that propose new methods for sparse functional object data and apply them to relevant real-world datasets, predominantly in a biomedical context