Abstract
This Ph.D. thesis dissertation addresses multi-resolution image decomposition, a key issue in signal processing that in recent years has contributed to the emergence of the JPEG2000 image compression standard. JPEG2000 incorporates many interesting features, mainly due to the discrete wavelet transform stage and to the EBCOT entropy coder. Wavelet analysis perform multi-resolution decompositions that decorrelate signal and separate information in useful frequency-bands, allowing flexible post-coding. In JPEG2000, decomposition is computed through the lifting scheme, the so-called second generation wavelets. This fact has focused the community interest on this tool. Many works have been recently proposed in which lifting is modified, improved, or included in a complete image coding algorithm. The Ph.D. thesis dissertation follows this research line. Lifting is analyzed, proposals are made within the scheme, and their possibilities are explored. Image compression is the main objective and it is principally assessed by means of coding transformed signal with EBCOT and SPIHT coders. Starting from this context, the work diverges in two distinct paths, the linear and the nonlinear one. The linear lifting filter construction is based on the idea of quadratic interpolation and the underlying linear restriction due to the wavelet transform coefficients. The result is a flexible framework that allows the creation of new transforms using different criteria and that may adapt to the image statistics. The nonlinear part is founded on the adaptive lifting scheme, which is extensively analyzed and as a consequence, a generalization of the lifting is proposed. The discrete version of the generalized lifting is developed leading to filters that achieve good compression results, specially for biomedical and remote sensing images