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We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques when applied to very sparse signals, and reconstruction accuracy of the same(More)
The Grassmann manifold G<sub>n,p</sub> (L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space L<sup>n</sup>, where L is either R or C. This paper considers the quantization problem in which a source in G<sub>n,p</sub> (L) is quantized through a code in G<sub>n,q</sub> (L), with p and q not necessarily the same.(More)
When building large-scale machine learning (ML) programs, such as massive topics models or deep networks with up to trillions of parameters and training examples, one usually assumes that such massive tasks can only be attempted with industrial-sized clusters with thousands of nodes, which are out of reach for most practitioners or academic researchers. We(More)
— We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques, and reconstruction accuracy of the same order as that of LP optimization(More)
We study the average distortion introduced by scalar, vector, and entropy coded quantization of compressive sensing (CS) measurements. The asymptotic behavior of the underlying quantization schemes is either quantified exactly or characterized via bounds. We also modify two benchmark CS reconstruction algorithms to accommodate quantization effects, and(More)
When building large-scale machine learning (ML) programs, such as massive topic models or deep neural networks with up to trillions of parameters and training examples, one usually assumes that such massive tasks can only be attempted with industrial-sized clusters with thousands of nodes, which are out of reach for most practitioners and academic(More)
A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank matrix consistent with the given observations. We show that this problem can be solved by searching for a column space that(More)
PURPOSE To explore and evaluate the protective effect of erythropoietin (EPO) on retinal cells of chemically induced diabetic rats after EPO was injected intravitreally at the onset of diabetes. METHODS Diabetes was induced in Sprague-Dawley rats by intraperitoneal injection of streptozotocin (STZ). At the onset of diabetes, a single intravitreal(More)
This paper considers the quantization problem on the Grassmann manifold with dimension n and p. The unique contribution is the derivation of a closed-form formula for the volume of a metric ball in the Grassmann manifold when the radius is sufficiently small. This volume formula holds for Grassmann manifolds with arbitrary dimension n and p, while previous(More)