We present a set-theoretic version of some basic dilation results operator theory. The we have considered are Wold decomposition, Halmos dilation, Sz. Nagy inter-twining lifting, commuting and non-commuting dilations, BCL theorem, etc. point out natural generalizations variations.

The separation of unobserved sources from mixed observed data is a fundamental signal processing problem. Most of the proposed techniques for solving this problem rely on independence or at least uncorrelation assumption for source signals. This paper introduces a technique for cases that source signals are correlated with each other. The method uses Wold decomposition principle for extracting ...

The problem of measuring perceptual similarity between images is addressed using a new image model based on the Wold decomposition. The model permits separate treatment of image components which correspond approximately to peri-odicity, directionality, and randomness. We compare its performance in an image search application to two other methods { one based on shift-invariant principle componen...

Sriram Subramanian1, Kap Luk Chan2, and Xiaoran Mo2 1 Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India 2 School of Electrical & Electronics Engineering, Nanyang Technological University, Singapore e-mail: [email protected] Abstract: Detecting faults in regular textures typically involves identi cation of local structures, such as knots, worm hol...

We give an example of the moderate deviations for the family (X n t) t≥0 , n ≥ 1 with ˙ X n t = a(X n t) + b(X n t) n √ n k+1 ηtn, where ηt is a stationary process obeying the Wold – decomposition: ηt = R t −∞ h(t − s)dN s with respect to a process Nt with homogeneous independent square integrable increments and 1/2 < k < 1.

An efficient texture representation for unsupervised segmentation is addressed based on the concept of Wold decomposition. Textures are described by the wavelet tuned to various scales and rotations to describe its deterministic component, and by the autogressive model to describe its indeterministic component. The wavelet features and the AR parameters capturing the perceptual properties, "per...