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EZW coding |
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The coding performance of EZW has since been exceeded by [[SPIHT]] and its many derivatives.
== Introduction ==
'''Embedded zerotree wavelet algorithm''' (EZW) is developed by J. Shapiro in 1993. This method enables scalable image transmission and decoding. And it is based on four key concepts. At first, it should be a discrete wavelet transform or hierarchical subband decomposition. Second, it should predict the absence of significant information when exploring the self-similarity inherent in images. Third it has entropy-coded successive-approximation quantization. Last, it is enable to achieve universal lossless data compression via adaptive arithmetic coding.
Besides, the EZW algorithm also contains the following features: 1) a discrete wavelet transform which can use a compact multiresolution representation in the image, 2) zerotree coding which provides a compact multiresolution representation of significance maps, 3) successive approximation for a compact multiprecision representation of the significant coefficients, 4) a prioritization protocol which the importance is determined by the precision, magnitude, scale, and spatial ___location of the wavelet coefficients in order, and 5) adaptive multilevel arithmetic coding which is a fast and efficient method for entropy coding strings of symbols.
== Embedded Zerotree Wavelet Coding ==
=== A. Encoding a coefficient of the significance map: ===
In a significance map, the coefficients can be representing by the following four different symbols:
==== 1. Zerotree root: ====
If the magnitude of a coefficient is less than a threshold T, and all its descendants are less than T, then this coefficient is called zerotree root. And if a coefficient has been labeled as zerotree root, it means that all of its descendants are insignificance, so there is no need to label its descendants.
==== 2. Isolated zero: ====
If the magnitude of a coefficient that is less than a threshold T, but it still has some significant descendants, then this coefficient is called isolated zero.
==== 3. Positive significant coefficient: ====
If the magnitude of a coefficient is greater than a threshold T at level T, and also is positive, than it is a positive significant coefficient.
==== 4. Negative significant coefficient: ====
If the magnitude of a coefficient is greater than a threshold T at level T, and also is negative, than it is a negative significant coefficient.
=== B. Defining threshold ===
==== 1. Initial threshold T<sub>0</sub>: (Assume C<sub>max</sub> is the largest coefficient.) ====
[[File:Threshold-0119.png|left|thumb|126x126px]]
==== 2. Threshold T<sub>i</sub> is reduced to half of the value of the previous threshold. ====
[[File:Threshold-01192.png|none|thumb|133x133px]]
=== C. Scanning order for coefficients: ===
'''Raster scanning''' is the rectangular pattern of image capture and reconstruction. Using this scanning on EZW transform is to perform scanning the coefficients in such way that no child node is scanned before its parent node. Also, all positions in a given subband are scanned before it moves to the next subband.
==See also==
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