Symmetric interpolatory framelets and their error correction

When transmitting images over practical communication channels, they are subject to packet loss and random errors due to the noisy nature of the channel. Errors and data loss are customarily recovered by means of error correction coding/decoding. In this paper, robust error-recovery algorithms are developed by utilizing the redundancy inherent in frame expansions. A new class of wavelet-type frames in signal space using (anti)symmetric waveforms is presented. The construction employs interpolatory filters with rational transfer functions. These filters have linear-phase. They are amenable to fast cascading or parallel recursive implementation. Experimental results recover images when (as much as) 60% of the packets are either lost or corrupted. The proposed approach inflates the size of the image through framelet expansion thus providing redundant representation of the image; this transform may be followed by compression. Finally, the frame-based error recovery algorithm is compared with a classical coding approach.