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Successive approximation (SA) quantization is part of many of the state-of-the-art image and video compression methods. We first make a review of it, starting from the classical optimality considerations of Equitz and Cover(1991) and then proceed to Mallat and Falzon (see IEEE Transactions on Signal Processing, vol.46, no.4, 1998) results concerning low bit-rate transform coding. We then develop a general theory of SA quantization which we refer to as o-expansions. This theory explains the published results obtained by both scalar and vector SA quantization methods, and indicates how further performance improvements can be obtained.