Signal compression and reconstruction using multiple bases representation
The problem of efficient signal communication at low data rates involves, in general, the encoding of the source for maximum data compression at the transmitter end, and the reconstruction using the received information and all the available a priori or side information at the receiver end. In this thesis, we propose an adaptive signal representation scheme, based on the use of multiple orthogonal basis sets, that exhibits very good potential in both the source encoding and the signal reconstruction problems. This representation leads naturally to the splitting of the signal into additive components, each of which has a simpler description than the original process. In addition, it exhibits a structure similar to that of codebook based coding. As a result, a very compact signal representation can be achieved.
A splitting procedure called recursive residual projection is proposed, and its performance evaluated for the separation of image-like signals into basis-defined “edge” and “texture” components. The coding of these components leads to lower rates than those for transform coding methods. In reconstruction, the representation can be considered as a well-behaved constraint. This allowed for the development of the corresponding unique projection operator, with application to general iterative reconstruction methods. In particular, we also proposed a noise tolerant version of the operator, a so-called soft projection operator, capable of achieving convergence under noisy measurement conditions. Computer simulations in the representation, coding, and reconstruction applications corroborate the usefulness of this proposed representation.