Related papers: Detection of low dimensionality and data denoising…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum.…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…
Low-Dose Computed Tomography (LDCT) technique, which reduces the radiation harm to human bodies, is now attracting increasing interest in the medical imaging field. As the image quality is degraded by low dose radiation, LDCT exams require…
This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…
We describe an approach for segmenting an image into regions that correspond to surfaces in the scene that are partially surrounded by the medium. It integrates both appearance and motion statistics into a cost functional, that is seeded…
In computer-aided diagnosis (CAD) focused on microscopy, denoising improves the quality of image analysis. In general, the accuracy of this process may depend both on the experience of the microscopist and on the equipment sensitivity and…
In this paper, we present a method for denoising and reconstruction of low-dimensional manifold in high-dimensional space. We suggest a multidimensional extension of the Locally Optimal Projection algorithm which was introduced by Lipman et…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
In recent years there has been a push to discover the governing equations dynamical systems directly from measurements of the state, often motivated by systems that are too complex to directly model. Although there has been substantial work…
Slice discovery methods (SDMs) are prominent algorithms for finding systematic weaknesses in DNNs. They identify top-k semantically coherent slices/subsets of data where a DNN-under-test has low performance. For being directly useful,…
Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be…