It is known that LOG–EXP transform based image compression algorithm proposed by SC Huang, LG Chen and HC Chang offers high Compression Ratio (CR) and high image quality compared to JPEG for any specified value of Peak-Signal to Noise Ratio (PSNR). In this paper, a modified LOG–EXP transform based image compression algorithm obtained by using arithmetic coding in the place of Huffman coding is proposed to reduce the computation time of the original LOG–EXP transform based algorithm. The proposed algorithm is found to be several times faster. It possesses almost the same CR and image quality as that of the algorithm of SC Huang, et. al. Also, FPGA implementation of the proposed algorithm is carried out on Xilinx Spartan 3E platform. The clock speed of the architecture has been found to be 96 MHz and the percentage resource utilization is 52%.