20-12-2012, 03:22 PM
Wavelet Zerotree Image Compression with Packetization
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Abstract
We describe a combined wavelet zerotree coding
and packetization method that provides excellent image compression
and graceful degradation against packet erasure. For
example, using 53-byte packets (48-byte payload), the algorithm
compresses the 512 512 gray-scale Lena image to 0.2 b/pixel
with a peak signal-to-noise ratio (PSNR) of 32.2 dB with no packet
erasure, and 26.3 dB on average for 10% packets erased.
INTRODUCTION
VARIOUS problems occur in packet switched networks.
Inadequate buffer space at network switches may cause
packets to be dropped during periods of congestion (packet
erasure). Packets may be received with corrupted bits, and
the decoder might make use of the erroneous data in the
packet. Error detection coding enables the decoder to discard
a corrupted packet, and retransmission protocols (ARQ) allow
the decoder to request that missing or discarded packets be sent
again. ARQ schemes introduce delay. Forward error correction
(FEC) techniques allow the decoder to correct a certain number
of errors, but they reduce the compression achievable because
extra bits are added. Error concealment techniques seek to
approximate (for example, by interpolation) the data from an
erased packet. The wavelet zerotree compression and packetization
method described in this letter is resilient to packet
erasures without the use of FEC or ARQ schemes. Previous
related work is [1]–[3].
PACKETIZABLE ZEROTREEWAVELET (PZW) COMPRESSION
The encoder begins by using a variation on the embedded
zerotree wavelet (EZW) and set partitioning in hierarchical
trees (SPIHT) coders [4], [5] to encode and store the entire
image to the target bit rate. The variation is essentially that of
[5], with the differences that arithmetic encoding is not used,
only four levels of wavelet decomposition are done, and each
“head” coefficient in the low-low band has three children, one
in each of the next directional bands, as in [4]. For a 512
512 image, there are 1024 head coefficients in the low-low
band; each has 3 (1 4 16 64) 255 descendants in
its tree. Each stored bit is associated with exactly one of the
1024 trees.
RESULTS AND CONCLUSIONS
The PZW algorithm was used to compress the 512 512
8 b/pixel gray-scale images, Lena and peppers. The initial
(progressive) wavelet coding was at 0.2 b/pixel. After packetization,
the actual rates achieved were 0.209 for Lena and 0.208
for peppers. These higher rates include the 14-b overhead for
each packet (10 b to specify the starting tree, and 4 b to
specify how many trees), as well as the effects of growing
and pruning trees within each packet. The PSNR’s achieved at
these rates (for four cases: all packets arriving, 1, 10, and 20%
packets erased) are shown in Table I along with the PSNR’s
for the SPIHT algorithm with and without arithmetic coding.
The PSNR’s were obtained by averaging the mean squared
errors for 10 000 random realizations of the packet erasures.
Note that for PZW the burstiness of the packet erasures makes
no difference, since all packets are equivalent a priori. That
is, if 20% of the packets are lost, it matters not which 20% are
lost. The decoder interpolates missing coefficients in the lowlow
band by averaging together as many of their immediate
eight-neighbors as are available.