Set Partition Coding: Part I of Set Partition Coding and Image Wavelet Coding Systems

  • Authors:
  • William A. Pearlman;Amir Said

  • Affiliations:
  • -;-

  • Venue:
  • Foundations and Trends in Signal Processing
  • Year:
  • 2008

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Abstract

The purpose of this two-part monograph is to present a tutorialon set partition coding, with emphasis and examples on imagewavelet transform coding systems, and describe their use in modernimage coding systems. Set partition coding is a procedure thatrecursively splits groups of integer data or transform elementsguided by a sequence of threshold tests, producing groups ofelements whose magnitudes are between two known thresholds,therefore, setting the maximum number of bits required for theirbinary representation. It produces groups of elements whosemagnitudes are less than a certain known threshold. Therefore, thenumber of bits for representing an element in a particular group isno more than the base-2 logarithm of its threshold rounded up tothe nearest integer. SPIHT (Set Partitioning in Hierarchical Trees)and SPECK (Set Partitioning Embedded blocK) are popularstate-of-the-art image coders that use set partition coding as theprimary entropy coding method. JPEG2000 and EZW (Embedded ZerotreeWavelet) use it in an auxiliary manner. Part I elucidates thefundamentals of set partition coding and explains the setting ofthresholds and the block and tree modes of partitioning. Algorithmsare presented for the techniques of AGP (Amplitude and GroupPartitioning), SPIHT, SPECK, and EZW. Numerical examples are workedout in detail for the latter three techniques. Part II describesvarious wavelet image coding systems that use set partitioningprimarily, such as SBHP (Subband Block Hierarchical Partitioning),SPIHT, and EZBC (Embedded Zero-Block Coder). The basic JPEG2000coder is also described. The coding procedures and the specificmethods are presented both logically and in algorithmic form, wherepossible. Besides the obvious objective of obtaining small filesizes, much emphasis is placed on achieving low computationalcomplexity and desirable output bitstream attributes, such asembeddedness, scalability in resolution, and random accessdecodability.This monograph is extracted and adapted from the forthcomingtextbook entitled Digital Signal Compression: Principles andPractice by William A. Pearlman and Amir Said, CambridgeUniversity Press, 2009.