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We propose a mixture of multiple linear models, also known as hybrid linear model, for a sparse representation of an image. This is a generalization of the conventional Karhunen-Loeve transform (KLT) or principal component analysis (PCA). We provide an algebraic algorithm based on generalized principal component analysis (GPCA) that gives a global and noniterative solution to the identification of a hybrid linear model for any given image. We demonstrate the efficiency of the proposed hybrid linear model by experiments and comparison with other transforms such as the KLT, DCT and wavelet transforms. Such an efficient representation can be very useful for later stages of image processing, especially in applications such as image segmentation and image compression.