Embedded zerotrees of wavelet transforms: Difference between revisions

Revision as of 15:56, 19 January 2016

Revision as of 05:44, 20 January 2016

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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) 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.

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=== 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 ====

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=== 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.) ====

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[[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.