整数变换方法因其较快的计算速度被国际图像和视频编码标准广泛采纳。现有基于连续正交函数系的整数变换方法不仅难以获得原始变换的准确整数形式，而且无法克服在非连续信号表达时出现的吉布斯震荡现象，降低了重构图像质量。为此，文中提出了基于非连续正交U系统的整数变换算法及其图像压缩方法。首先，采用分段积分法和施密特正交化法计算出U系统的2维正交变换矩阵，提取行向量的缩放因子得到整数矩阵；接着，建立整数U矩阵的可逆正交变换方法，使用整数矩阵将离散图像信息的能量集中到少量数据集，同时将缩放因子与量化步骤合并以减轻计算负担；然后，采用矩阵分解法将整数U矩阵分解为稀疏矩阵的乘积，从而实现图像变换的快速计算；最后，设计基于整数U变换模块和逆变换模块的图像压缩方法，用于减轻图像存储和传输压力。实验结果表明：文中方法与其他相关方法相比，可以降低图像可逆变换的截断误差；在图像和视频压缩实验中，在相同的压缩率下文中方法获得的压缩图像质量更高，而且快速变换方法可以有效地节省运算时间。

The integer transform methods are widely adopted in international image and video coding standards because of its fast calculation speed. The existing integer transform methods based on the continuous orthogonal function system not only struggle to obtain the exact integer form of the original transform, but also fails to overcome the Gibbs oscillation phenomenon in the discontinuous signal representation, thus reduces the reconstructed image quality. This paper proposed a new integer transform algorithm and its image compression method based on discontinuous orthogonal U-system. Firstly, the piecewise integration and the Gram-Schmidt process were used to calculate the two-dimensional orthogonal matrix of the U-system, and the scaling factors of row vectors were extracted to obtain the integer matrix. Secondly, the reversible integer U transform was established and the integer matrix was applied to concentrate the energy of images into a small amount of data sets, while merging scaling factors with quantization to reduce computational burden. Then, the fast integer U transform was achieved by using matrix decomposition and sparse matrices. Finally, the integer U transform module and inverse transform module were designed to alleviate the pressure of image storage and transmission. Experimental results show that the proposed method can reduce truncation errors of reversible image transform compared with related algorithms; the new method obtains higher compression image quality in image and video compression experiments, and the fast transform algorithm effectively saves computational time.