By expanding the signal in wavelet series , we get its approximation up to a desired scale . and a cost function for representing the error between the signal and its approximation is established . we then optimize the cost function by improved genetic algorithms in order to obtain the global optimal orthogonal wavelet basis 通过将信号用小波级数展开后得到其在某个期望尺度上的近似表示，由此建立一个表达信号与其近似之间误差的代价函数，然后我们利用改进遗传算法最优化此代价函数以获得全局最优的正交小波基。
We study the design of haar wavelet for scale = a ( a2 ) and present a decomposition and reconstruction algorithm in chapter 3 . secondly , in chapter 4 we study the design of orthonormal mutiwavelets of multiplicity r with scale = a ( a2 ) . by the factorization theory , we give parametric expressions for orthonormal causal fir multifilter banks of r = 2 and scale = 4 , and we found the length of scaling function can be controlled by the parameters . finally , we provide the error analysis between discrete multiwavelet transform coefficients and continue multiwavelet transform coefficients 由于多小波变换系数的计算是直接与其预滤波方式相联系的，而在单小波变换系数计算中之所以能由近似表示就是因为尺度函数具有低通特性和平移正交性，由此我们研究了能满足以上要求的预滤波，并对离散小波变换系数和连续小波变换系数之间的差异作了分析，从误差分析结果我们可以预见：为了减少误差我们可以通过对预滤波的进一步设计来控制。
The framework suppose that the image ' s semantic feature can be expressed by using a multi - level attribute tree , and the probability of a certain image having a certain attribute can be estimated by interpolation method using the neighboring image ' s value . here , the neighboring relation refers to the neighboring in the low - level feature space 该框架假定图像的语义特征可用多层属性树来近似表示，并且图像拥有某个属性的概率值可由相邻的图像的概率值进行插值估计，框架中的相邻指图像在底层特征空间的相邻。
