It is known that transform techniques do not represent an optimal way in which to code a signal in terms of theoretical rate distortion bounds. A signal may be coded more efficiently if side information is included with the signal during transmission. This side information can then be used to reconstruct the image at some later time.

In this thesis, the type of transform coding used is Multiple Bases Representation (MBR). This coding scheme is known to perform better than transform coding that uses a single basis. The method of Projection Onto Convex Sets (POCS) is used to reconstruct an approximation to the MBR signal using the side information. Thus, any number of constraints may be used as long as they form closed and convex sets and the side information is a priori knowledge required to implement projections onto the defined closed and convex sets.

Several closed and convex sets are examined including the MBR, positivity, sign, zero crossing, minimum increase, and minimum decrease constraints. Constraints that tend to limit energy are not as effective as constraints that introduce energy into the signal especially when the observed image is used as the initialization vector.

When a different initialization vector is used, the POCS reconstruction performs considerably better. Two initialization vectors are proposed; the observed signal plus white noise and the observed signal plus a constant. The performance of POCS with initialization by the observed signal plus a constant is superior to that when using the observed signal only.

One nonconvex constraint is considered. The Laplacian histogram constraint requires other convex constraints to help ensure convergence of the reconstruction algorithm, but produces good quality images.