In these days, as the size of images are increasing, compression has become very important and common way to minimize the amount of storage necessary for images. The purpose of image compression is to reduce the size to achieve savings in storage and communication cost and at the same time, to keep most of the information contained in the original image. In JPEG standard which is frequently used for still images, Discrete Cosine Transform (DCT) is the most popular lossy technique used to decompose the image into low frequency and high frequency coefficients. This allows further image compression operation to occur. In this paper we have compared different methods of calculating DCT having different complexity and different number of resources used. Out of them using an early detection algorithm in a distributed arithmetic architecture can achieve reduction in computation and speed up the image compression more efficiently.