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Resolution scalability in images and video is performed in one of two ways: either by the method of Laplacian pyramids, or by an iterated subband filter bank such as the wavelet transform. In the case of the former, the method of Laplacian pyramids is an oversampled transform that does not offer true scalability because the cost of encoding increases for each additional level of resolution that is embedded.In contrast, the wavelet transform offers true scalability, with no overhead for arbitrary levels of resolution. However, the wavelet transform suffers from poor aliasing suppression capabilities, which is a fundamental limitation of the filter design of critically sampled subband transforms.In this thesis we present three novel transforms that are scalable, critically sampled, and offer superior aliasing suppression to the wavelet transform. We also provide comparison with state of the art in pyramid-based transforms.

Resolution scalability in images and video is performed in one of two ways: either by the method of Laplacian pyramids, or by an iterated subband filter bank such as the wavelet transform. In the case of the former, the method of Laplacian pyramids is an oversampled transform that does not offer true scalability because the cost of encoding increases for each additional level of resolution that is embedded.In contrast, the wavelet transform offers true scalability, with no overhead for arbitrary levels of resolution. However, the wavelet transform suffers from poor aliasing suppression capabilities, which is a fundamental limitation of the filter design of critically sampled subband transforms.In this thesis we present three novel transforms that are scalable, critically sampled, and offer superior aliasing suppression to the wavelet transform. We also provide comparison with state of the art in pyramid-based transforms.