Compressed sensing (CS) methods can be used to reconstruct MRI signals from highly undersampled data [1]. Recent studies have shown that selecting gridded samples using a Poisson disk sampling pattern yields improved reconstructions over the traditional uniform random sampling of a Cartesian grid [2]. We extend this work by evaluating the effects of Poisson disk sampling of a continuous k-space...

Monotone systems preserve a partial ordering of states along system trajectories and are often amenable to separable Lyapunov functions that are either the sum or the maximum of a collection of functions of a scalar argument. In this paper, we consider constructing separable Lyapunov functions for monotone systems that are also contractive, that is, the distance between any pair of trajectories...

Abstract We consider the problem of computing (two-sided) Hausdorff distance between unit $\ell _{p_{1}}$ ℓ p 1 and _{p_{2}}$ 2 norm balls in finite dimensional Euclidean space for $1 \leq p_{1} &lt; p_{2} \infty $ ≤ <m...

Fast indexing in time sequence databases for similarity searching has attracted a lot of research recently. Most of the proposals, however, typically centered around the Euclidean distance and its derivatives. We examine the problem of multimodal similarity search in which users can choose the best one from multiple similarity models for their needs. In this paper, we present a novel and fast i...

In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation procedure can then be evaluated using the bottleneck distance between the estimated persistent homology and the true persistent homology. The connection to sta...

Hawkins (1980) defines an outlier as “an observation that deviates so much from other observations as to arouse the suspicion that it was generated by a different mechanism”. To identify data outliers, a classic multivariate outlier detection approach implements the Robust Mahalanobis Distance Method by splitting the distribution of distance values in two subsets (within-the-norm and out-of-the...

In this paper, we present a novel approach for image database retrieval, which is a developing field with growing interest. Many features (e.g. color, shape, texture) can be considered to find similar images in the database for a given query image. We recommend a novel way of measuring the similarity which is based on calculating the norm of the similarity vectors (that is the distance between ...

In the last lecture we defined metric spaces, normed spaces, and considered the distortion resulting from certain embeddings. In particular, we proved that l1 norms cannot always be embedded isometrically into l2 by considering a specific four-point l1 norm and showing that it requires at least √ 2 distortion. Today’s lecture further explores the 1 norm. We see a couple of interesting examples ...

If K is a 0-symmetric, bounded, convex body in the Euclidean n-space R (with a fixed origin O) then it defines a norm whose unit ball is K itself (see [12]). Such a space is called Minkowski normed space. The main results in this topic collected in the survey [16] and [17]. In fact, the norm is a continuous function which is considered (in the geometric terminology as in [12]) as a gauge functi...

• Positivity: N(v) ≥ 0 with equality if and only if v = 0. • Positive Homogeneity: N(αv) = |α|N(v). • Triangle Inequality: N(x1 + x2) ≤ N(x1) +N(x2). If N is a norm for V then we call ρ N (x1, x2) := N(x1−x2) the associated distance function (or metric) for V . A vector space V together with some a choice of norm is called a normed space, and the norm is usually denoted by ‖ ‖. If V is complete...