General Embedded Quantization for Wavelet-Based Lossy Image Coding

Abstract

Abstract-Embedded quantization is a mechanism employed by many lossy image codecs to progressively refine the distortion of a (transformed) image. Currently, the most common approach to do so in the context of wavelet-based image coding is to couple uniform scalar deadzone quantization (USDQ) with bitplane coding (BPC). USDQ+BPC is convenient for its practicality and has proved to achieve competitive coding performance. But the quantizer established by this scheme does not allow major variations. This paper introduces a multistage quantization scheme named general embedded quantization (GEQ) that provides more flexibility to the quantizer. GEQ schemes can be devised for specific decoding rates achieving optimal coding performance. Practical approaches of GEQ schemes achieve coding performance similar to that of USDQ+BPC while requiring fewer quantization stages. The performance achieved by GEQ is evaluated in this paper through experimental results carried out in the framework of modern image coding systems.

2-Step Scalar Deadzone Quantization for Bitplane Image Coding

“…Only the magnitude of coefficients is depicted (omitting the sign) since symmetry about zero is assumed. (a) and (b) depict the USDQ+BPC scheme and the practical GEQ [27], respectively. The procedure continues in this fashion until the width of all intervals is ∆, which occurs when all bitplanes are coded.…”

“…different quantizers of K quantization stages. Our previous work [27] explores the efficiency of GEQ exhaustively, disclosing those schemes that achieve the best rate-distortion performance. Inspired by the design of such quantizers, then a practical approach of GEQ is proposed and tested in the framework of JPEG2000.…”

“…The practical GEQ proposed in [27] produces quantization intervals of width twice larger for coefficients |ω| ≥ W/3 than for coefficients |ω| < W/3. Fig.…”

“…Nonetheless, USDQ+BPC is not specifically designed to achieve optimal coding performance for a selected range of decoding rates, and it permits only small variations on the quantization scheme. Motivated by these issues, our previous work [27] introduced a more flexible scheme named general embedded quantization (GEQ). The focus of that work is to explore the performance, in terms of coding efficiency and quantizer complexity, that can be achieved by GEQ.…”

“…Unfortunately, the approach of [27] requires structural modifications when introduced in conventional codecs. Mainly, these modifications are needed due to 1) the abandonment of the indices' binary representation, 2) a different order of coding passes, and 3) the selective operation of the quantizer on coefficients that vary at each stage.…”