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In this paper, we propose a orthonormal finite ridgelet packet transform. An image coding algorithm based on a rate distortion optimized orthonormal finite ridgelet packet transform (OFRPT) decomposition and on a block-partitioning coding scheme which quantizes each subband separately is proposed. In this way, our algorithm naturally overcomes the difficulty in defining parent-child relationships for wavelet-based ridgelet packets subbands, which exists in the zerotree based methods. The main merit of the proposed method is that the ridgelet transform can provide optimally sparse representation of objects with singularities along straight edges and the orthonormal finite ridgelet packet (OFRPT) can decompose the high frequency parts of the images which are not decomposed in discrete wavelet transform. The experimental results show that the proposed algorithm significantly outperforms SPIHT and JPEG2000 schemes in novel image with straight lines significantly or curve lines significantly coding, in terms of both PSNR and visual quality.