2代Bandlet变换中耗时最多的是四叉树构建和最优几何方向选取，而且原算法准确度也不高。为了解决这个问题，本文提出基于进退法选取最优几何方向算法；然后又提出了基于遗传算法的最优方向选取算法；最后把这两种方法结合在一起可以取得更好的结果。同时改进了原算法中的自底向上的四叉树算法为自顶向下的四叉树算法，提高了对特定图象处理的速度。最后本文把改进的算法应用到去噪，压缩和图像增强中，取得了较好的效果。并对算法的时间和空间复杂度进行了分析。“,”Construction of quadtree and selection of the best geometry direction (BGDS) are the most time-consuming parts in 2G Bandelet Transform, and the result of original method is not the best. To solve the problem, in this paper, a BGDS method based on the advance and retreat method was presented firstly;then the genetic algorithm for BGDS was proposed;finally, these two methods were combined to get better results. Experiments show that these three methods all have some advantages compared with original method. Furthermore, the original bottom-up quadtree algorithm was improved to a top-down quadtree algorithm, which has some advantages in processing some special images. In the ending of this paper, the application of improved bandelet based on genetic algorithm was presented, and the time complexity and space complexity of these algorithms were compared.