A runtime reconfigurable very-large-scale integration （VLSI） architecture for image and video scaling by arbitrary factors with good antialiasing performance is presented in this paper. Video scal- ing is used in a wide range of applications from broadcast, medical imaging and high-resolution video effects to video surveillance, and video conferencing. Many algorithms have been proposed for these applications, such as piecewise polynomial kernels and windowed sinc kernels. The sum of three shifted versions of a B-spline function, whose weights can be adjusted for different applications, is adopted as the main filter. The proposed algorithm is confirmed to be effective on image scaling ap- plications and also verified by many widely acknowledged image quality measures. The reconfigu- rable hardware architecture constitutes an arbitrary scaler with low resource consumption and high performance targeted for field programmable gate array （FPGA） devices. The scaling factor can be changed on-the-fly, and the filter can also be changed during runtime within a unifying framework.
The acquired hyperspectral images （HSIs） are inherently attected by noise wlm Dano-varylng level, which cannot be removed easily by current approaches. In this study, a new denoising method is proposed for removing such kind of noise by smoothing spectral signals in the transformed multi- scale domain. Specifically, the proposed method includes three procedures： 1 ） applying a discrete wavelet transform （DWT） to each band; 2） performing cubic spline smoothing on each noisy coeffi- cient vector along the spectral axis; 3 ） reconstructing each band by an inverse DWT. In order to adapt to the band-varying noise statistics of HSIs, the noise covariance is estimated to control the smoothing degree at different spectra｜ positions. Generalized cross validation （GCV） is employed to choose the smoothing parameter during the optimization. The experimental results on simulated and real HSIs demonstrate that the proposed method can be well adapted to band-varying noise statistics of noisy HSIs and also can well preserve the spectral and spatial features.
Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s 1.We call f the generator of the operators In and It.It is well known that there are many results on operators In and It.But there remain some important problems to be further explored.For application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative operators.In this paper,we focus on the available generator in the class of spline functions.We shall see that not all spline functions can be used to construct available generators.Fortunately,we do find a spline function in S,of degree m-1,where m is even and S is a class of splines.But for odd m the problem is still open.Results on spline functions in this paper are new.
CHEN HanLin Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
