Compression of Two-Dimensional Band-Limited Signals Using Sub-Sampling Theorems

Abstract

Non-uniform versions of the classical sampling theorem are applied to the compression of discrete two-dimensional (2D) signals. It is shown that the data rate of a hand-limited 2D signal can be reduced directly by sub-sampling methods. This means that the algorithm for compression is extremely simple, though the recovery of the original signal becomes complex. The procedure for reconstruction is derived by using linear filtering operations and 2D sampling rate alterations. The whole sub-sampling/reconstruction system is formulated in the form of a 2D multirate filter bank. Not every sub-sampling method allows for the perfect reconstruction of the original signal. A sufficient condition on the sub-sampling scheme is derived which would make reconstruction feasible. In theory, the reconstruction of the missing samples requires the use of piece-wise constant filters, but in practice their ideal responses can be approximated by FIR filters.

Indexing terms:

• Band-limited 2D signals
• FIR filter