JPEG (Joint Photographic Experts Group) is an international standard to compress and store digital color images . Given a color image that was previously JPEG-compressed in some hidden color space, we aim to estimate this unknown compression color space from the image. This knowledge is potentially useful for color image enhancement and JPEG re-compression. JPEG operates on the discrete cosine transform (DCT) coefficients of each color plane independently during compression. Consequently, the DCT coefficients of the color image conform to a lattice structure. We exploit this special geometry using the lattice reduction algorithm from number theory and cryptography to estimate the compression color space. Simulations verify that the proposed algorithm yields accurate compression color space estimates.