酉基和非交换小波

传统小波分析研究了Hilbert函数空间上确定的正交基．利用非交换小波方法，构造了小波基．证明了在非交换条件下，能够选择标准正交基向量作为任何固定序的酉算子．使用算子代数上的酉基研究了二元函数的代表，并讨论了其收敛性,构造了M2(R)上的酉基，并用张量积方法构造了M2^n(R)上的酉基．用这组基对图形进行分解，并将分解后的系数矩阵用于图像信息的隐藏与加密．

Unitary and Noncommutative Wavelet

In the classical wavelet theory,study on certain orthogonal basis of Hilbert spaces of functions.The noncommutative wavelet method to construct wavelet basis is used.In noncommutative case,orthonormal base vectors can be chosen to be unitary operators of any fix order.The unitary basis on an operator algebra to study of representations of two dimensional functions is used and the certain convergence is discussed.Next,a group of unitary basis is constructed,and form the unitary basis by tensor product.By this group basis,image is decomposed,and coefficient matrix by decomposing image is used to encipher and hide image information.