It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of the wavelet coefficients. Following an innovation modeling approach, we identify a general class of finite-variance self-similar sparse rand...

Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.

let $g$ be a group and $h$ a subgroup of $g$‎. ‎ $h$ is said to have semi-$pi$-property in $g$ if there is a subgroup $t$ of $g$ such that $g=ht$ and $hcap t$ has $pi$-property in $t$‎. ‎in this paper‎, ‎investigating on semi-$pi$-property of subgroups‎, ‎we shall obtain some new description of finite groups‎.

Abstract We provide the structure of unit group $${\mathbb {F}}_{p^k}S_n$$ F p k S n , where $$p>n$$ > is a prime and $$S_n$$ denotes symmetric on n l...

This paper presents a wavelet-based approach for the design of the finite impulse response (FIR) notch filter with controlled null width. The M-band P-regular wavelet filters are employed to constitute the null space of the derivative constraint matrix. Taking advantage of the vanishing moment property of the wavelet filters, the proposed method controls the null width of the notch filter by ad...

In linear approximation by wavelet, we approximate a given function by a finite term from the wavelet series. The approximation order is improved if the order of smoothness of the given function is improved, discussed by Cohen (2003), DeVore (1998), and Siddiqi (2004). But in the case of nonlinear approximation, the approximation order is improved quicker than that in linear case. In this study...

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.