小波变换是一种强有力的图像消噪方法，选取合适的小波变换具有重大意义。k次V系统是一类在L2［0,1］空间上新建立的完备正交系，它由分段k次多项式组成，具有多小波（multi-wavelet）的多分辨（multi-resolution）特性，特别是它的基函数中既有连续的函数又有间断的函数，这是它与其他经典正交系的不同。文中利用线性V系统及其相应的正交V变换，探索V系统在数字图像消噪中的应用。将V系统的消噪效果与经典的小波消噪进行比较，采用PSNR作为评价标准，利用MATLAB进行大量的试验，结果表明V系统对高斯白噪声、椒盐噪声以及乘性斑点噪声的消除均有明显的优势。

Wavelet transform is a powerful method in image denoising, and it is of great significance to select an appropriate kind of wavelet transform. V-system of degree k is a class of complete orthogonal function system on L2［0,1］,which is composed of sub-function of degree k, with the characteristics of the multi-resolution of multi-wavelet. Particularly, its basic function contains both continuous and discontinuous functions, which makes it different from classic orthogonal function system. In this article, a new kind of orthogonal discrete transform called DVT is proposed, and the application of DVT in image denoising is studied. The comparisons of the DVT with wavelet transform in image denoising are given. Using PSNR as evaluation criteria and using MATLAB processing to carry out a lot of experiments, the comparison results indicate that the linear DVT has obvious advantages in the denoising of Gaussian noise, salt & pepper noise and speckle noise.