Images are very important documents nowadays. To work with them in some applications they need to be compressed, more or less depending on the purpose of the application. To reduce transmission cost and storage requirements, competent image compression schemes without humiliation of image quality are required. Several image coding techniques were developed so far for both lossless and lossy image compression. Extensions of 1-D transforms such as wavelet transform have limitations of capturing geometry of image edges. Functions that have discontinuities along straight lines cannot be effectively represented by normal wavelet transforms but natural images have geographic lines such as edges, textures which cannot be well reconstructed if compression is done by 1-D Transforms. Nowadays image coding is done, using Curvelet Transform since it supports different orientations of image textures. An investigation is done on various types of image coding techniques based on Curvelet Transform that exist. This paper deals with study of image compression techniques using Curvelet Transform based on Support vector machine and Core vector machine with their performance results.