Methods exploring the application of support vector machine learning (SVM) to still image compression are detailed in both the spatial and frequency domains. In particular the sparse properties of SVM learning are exploited in the compression algorithms. A classic radial basis function neural network requires that the topology of the network be defined before training. An SVM has the property that it will choose the minimum number of training points to use as centres of the Gaussian kernel functions. It is this property that is exploited as the basis for image compression algorithms presented in this book. Several novel algorithms are developed applying SVM learning to both directly model the colour surface and model transform coefficients after the surface has been transformed into the frequency domain. It is demonstrated that compression is more efficient in frequency space. In the frequency domain, results are superior to that of JPEG. For example, the quality of the industry standard 'Lena' image compressed 63:1 for JPEG is slightly worse quality than the same image compressed 192:1 with the RKi-1 algorithm detailed in this book.