This paper presents a theoretical analysis and computing technique for performing image data compression in orthogonal spline space. First, we define the orthogonal spline basis functions which are derived from the subdivision of the discrete cosine transform. The number of subdivided blocks is the integer power of 2. In this paper, we present the detailed analysis of the bi-orthogonal and the quad-orthogonal spline spaces. Fast image compression and decompression algorithms in these spaces are given and simulated with examples. Based on the simulation results, one can conclude that this new image compression method is superior to the ordinary discrete cosine transform; i.e., it can retain more high-frequency details with less artifact and noise. Compared to the subband coding technique, this new method is still favorable both in terms of image detail and buffer size. In short, this new compression method reproduces better image quality for a prescribed data compression ratio in the reconstructed image.