| This research investigates the concept of the minimum coefficient rate of random processes defined by Campbell, and develops a theory that uses the coefficient rate result to estimate the code rate for the side information in transform coding. For adaptive transform coding schemes, how to efficiently encode the side information is the key to improving coding performance, yet no one has given a general theory on how to characterize the side information and how to estimate the code rate for it. Using the significance map of transform coefficients as a representation of the side information, we first prove that encoding the side information requires the knowledge of the distributions of the coefficients, which is generally very difficult to obtain in practical coders. To avoid this problem, current existing coders design coding strategies based on certain assumptions on the behavior of the transform coefficients which also limits the use of these coding schemes. Motivated by Campbell's result and some coding schemes that use spectral entropy or the theoretical dimension of signals, we establish a connection between the coefficient rate and the side information in transform coding and prove that the spectral entropy can be used to estimate the code rate used for the side information. An image coder based on this theory is implemented and its performance is compared with a more conventional transform coder which uses optimal bit allocation. We then investigate how to use the coefficient rate result in embedded coding, where encoding the significance map is the key to achieving better coding performance. Analysis shows that the spectral entropy can also be used to estimate the average code rate for the significance map in embedded coders. A general embedded approach is described and experimental results show that coders using such an approach can be very competitive compared with single-stage coders. |
