Orthonormal Motion-Adaptive Transforms for Image Sequences

Sammanfattning: In this thesis, we propose and discuss a class of motion-adaptive transforms (MAT) to describe the temporal correlation in image sequences for compression. The temporal correlation is based on motion models, and undirected graphs are used to represent this correlation in image sequences. The transforms are adaptive to general motion fields. Hence, they avoid the predict-update mismatch of the classic block-motion lifting schemes in processing connected and disconnected pixels. Moreover, the proposed transforms are orthonormal for general motion field, and thus, they permit energy conservation and perfect reconstruction.As we represent the motion-connected signals by graphs, we introduce a graph-based covariance matrix model and use the associated eigenvector matrix for compression. As the proposed covariance model is closely related to the graph, the relation between the covariance matrix and theLaplacian matrix is studied and the associated eigenvector matrices are discussed. The class of MAT is constructed by using so-called scale factors.We show that the scale factors determine a relevant subspace of the signal representation.Hence, we propose a subspace-constrained transform, which achieves optimal energy compaction given the subspace constraint. On the other hand, the resulting basis vectors are signal dependent.To construct practical transforms without using covariance matrices, we consider two types of incremental transforms over graphs, namely the uni-directional orthogonal transform (Uni-OT) and the bidirectional orthogonal transform (Bi-OT). In addition, fractional-pel MAT is proposed to further extend the class of MAT. Our fractional-pel MAT can incorporate a general interpolation filter into the basis vectors, while offering perfect reconstruction, orthogonality, and improved coding efficiency.