The Karhunen-Loeve (KL) transform is widely used technique for image compression or clustering analysis. Since KL transform is a reversible linear transform, a novel cryptosystem is developed to provide confidentiality service for images. The original image (x), in the form of square matrix, is given as input to the KL transform which in turn produces the encrypted image (y) and the decryption ...

Let G = SpecA be a linearly reductive group, and wG ∈ A ∗ be G-invariant and wG(1) = 1. We establish the harmonic analysis on G and we compute wG when G = Sln, Gln, On, Sp2n, by geometric arguments and by means of the Fourier transform. Introduction An affine k-group G = SpecA is semisimple if and only if A splits in the form A = k ×B∗ as k-algebras, where the first projection π1 : A → k is the...

the 9/7 Filter for Image Blocks Hongying Meng and Zhihua Wang A new fast spatial Combinative lifting algorithm (SCLA) of the wavelet transform with the 9/7 filter for image blocks is proposed. In comparison with its lifting-based implementation, the multiplication is reduced by a ratio of 5/12. The SCLA can speed up the implementation of the wavelet transform. Introduction: The popular 9/7 filt...

An example of application of the wavelet transform to electrocardiography is described in the paper. The transform is exploited as a first stage of an ECG signal compression algorithm. The signal is decomposed into particular timefrequency components. Some of the components are removed because of their low influence to signal shape due to nonstationary character of ECG. Resulted components are ...

feat V be a binary linear (n, k) code defined by a check matrix H and let h(x) be the characteristic function for the set of columns of H . Connections between the Walsh transform of h(x) and the weight distributions of all translates of the code are obtained. Explicit formulas for the weight distributions of translates are given for small weights i(i < 8). The computation of the weight distrib...

Daoqiang Zhang, Songcan Chen * Department of Computer Science and Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, P.R. China. Abstract: A novel matrix K-L transform (MatKLT) is proposed as an extension to the conventional K-L transform (KLT) in this paper for fast image compression. Experimental results on 18 publicly available benchmark images show that the MatKL...

We consider a processor shared M/M/1 queue that can accommodate at most a finite number K of customers. We give an exact expression for the sojourn time distribution in the finite capacity model, in terms of a Laplace transform. We then give the tail behavior, for the limit K → ∞, by locating the dominant singularity of the Laplace transform. keywords: finite capacity, processor sharing, sojour...

We present several wavelet transform algorithms and their applications in astronomical image processing (restoration, object detection , compression, etc.). Extensive literature exists on the wavelet transform and its application (Chui 1992; Daubechies 1992; Meyer 1989). A discrete wavelet transform approach can be obtained from multiresolution analysis (Mallat 1989). Multiresolution analysis r...

Many combinatorial problems can be formulated as “Can I transform configuration 1 into configuration 2, if certain transformations only are allowed?”. An example of such a question is: given two k-colourings of a graph, can I transform the first k-colouring into the second one, by recolouring one vertex at a time, and always maintaining a proper k-colouring? Another example is: given two soluti...

where ∆ is the Laplace operator. Here σ > 0 is a constant (the diffusion constant). It has dimensions of distance squared over time, so H0 has dimensions of inverse time. The operator exp(−tH0) for t > 0 is an self-adjoint integral operator, which gives the solution of the heat or diffusion equation. Here t is the time parameter. It is easy to solve for this operator by Fourier transforms. Sinc...