||In fractal image compression the encoding step is computationally expensive. We present a new technique for reducing the encoding complexity. It is lossless, i.e., it does not sacrifice any image reconstruction quality for the sake of speedup. It is based on a codebook coherence characteristic of fractal image compression and leads to a novel application of the Fast Fourier Transform based cross-correlation. The method provides a new conceptual view of fractal image compression. This paper focuses on the implementation issues and presents the first empirical experiments analyzing the performance benefits of the convolution approach to fractal image compression depending on image size, range size, and codebook size. The results show acceleration factors for large ranges up to 23 (larger factors possible), outperforming all other currently known lossless acceleration methods for such range sizes.