Embedded zerotrees of wavelet transforms: Difference between revisions

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'''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) aA discrete wavelet transform which can use a compact multiresolution representation in the image, .

(2) zerotreeZerotree coding which provides a compact multiresolution representation of significance maps,.

(3) successiveSuccessive approximation for a compact multiprecision representation of the significant coefficients, .

(4) aA 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.

(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:. With using these symbols to represent the image information, the coding will be less complication.

==== 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 ===

The threshold using above can be defined as the type below.

==== 1. Initial threshold T₀: (Assume C_max is the largest coefficient.) ====