The authors examine and describe an implementation of a fractal compression method on optical satellite images. The basic principle is that an image can be reconstructed by using the self similarities in the image itself. The satellite image is first partitioned into a set of non-overlapping ranges. For each range, a “best matching” domain block would be found and a set of affine transformation would be performed. The compression would be obtained by storing only the descriptions of this transformation. The fractal compression method is implemented on two images, a complicated city image and a simple coastal area image. Using a fractal algorithm, the data integrity of the coastal area image was maintained with a peak signal-to-noise ratio (PSNR) of approximately 34.9 dB while achieving a compression ratio of 172:1. A novel approach of using a combination of fractal and wavelet algorithms for data compression is also described.