Entanglement renormalization is a unitary real-space scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they particularly well-suited to describing systems at criticality. In this work we show how construct Gaussian bosonic that implement entanglement for ground states of arbitrary free chains. construction based on wavelet theory, the dispersion relation Hamil...

Wavelet-based image denoising algorithm depends upon the energy compaction property of wavelet transforms. However, for many real-world images, we cannot expect good energy compaction in a single wavelet domain, because most real-world images consist of components of a variety of smoothness. We can relieve this problem by using multiple wavelet bases to match different characteristics of images...

The wavelet representation using orthonormal wavelet bases has received widespread attention. Recently M-band orthonormal wavelet bases have been constructed and compactly supported M-band wavelets have been parameterized 15, 12, 32, 17]. This paper gives the theory and algorithms for obtaining the optimal wavelet multiresolution analysis for the representation of a given signal at a predetermi...

Orthonormal wavelet expansions are applied to atmospheric surface layer velocity and temperature measurements above a uniform bare soil ‘surface that exhibit a long inertial subrange energy spectrum. In order to investigate intermittency effects on Kolmogorov’s theory, a direct relation between the &h-order structure function and the wavelet coefficients is derived. This relation is used to exa...

There has been considerable recent interest in using wavelets to analyze time series and images that can be regarded as realizations of certain oneand two-dimensional stochastic processes. Wavelets give rise to the concept of the wavelet variance (or wavelet power spectrum), which decomposes the variance of a stochastic process on a scale-by-scale basis. The wavelet variance has been applied to...

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...