Data Description in Subspaces

Frameness bound for frame of subspaces

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.

Extending Functions in the Model Subspaces of H^2(R) to C

The backward shift on H

z on the classical Hardy space H. Though there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds E ⊂ H for which BE ⊂ E . When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation deve...

The Adaptive Subspace Map for Image Description and Image Database Retrieval

In this paper, a mixture-of-subspaces model is proposed to describe images. Images or image patches, when translated, rotated or scaled, lie in low-dimensional subspaces of the high-dimensional space spanned by the grey values. These manifolds can locally be approximated by a linear subspace. The adaptive subspace map is a method to learn such a mixture-of-subspaces from the data. Due to its ge...

Matrix Method for Lcmm — Connection between Subspaces of Reference Points

The article describes the transplantation of Matrix Method as an assessment of accuracy of coordinate measurement for Large CMM. The method of the synthetic description of the accuracy is used successfully for small and medium-sized CMMs. It is implemented for large measurements as research project nr: PB 5T07/D03824. The issue involves many problems, especially from a technical point of view. ...