Design of general block oriented expansions for efficient signal representation

The reconstruction stage of ordinary transform coders performs a linear combination of the columns of the inverse transform matrix in proportion given by the quantized transform coefficients. At low bit rates only a small number of vectors contribute in this linear combination. Here we address the problem of designing reconstruction matrices for such coders, but we remove the constraints of traditional transform coders. We end up with matrices that are not orthogonal, nor necessarily nonsingular. It is demonstrated that the approximation capabilities of the corresponding linear combinations are superior to those obtained when using the discrete cosine transform (DCT) or for that matter the Karhunen-Loeve transform (KLT) computed for the signals at hand. This statement is verified for a selection of synthetically generated as well as real-life signals