Zerotree Coding Research Articles

Comparison of different image subband coding methods at low bit rates

Two image subband coding methods are introduced as combinations of trellis-coded quantization (TCQ) with zerotree and stack-run coding. These TCQ-based image coding algorithms are compared, at low bit rates, with the set partitioning in hierarchical trees and stack-run scalar quantization-based image coding algorithms. Direct use of TCQ with zerotree or stack-run coding methods is found to provide little or no improvement in rate-distortion performance compared to scalar quantization.

Wavelet lossless compression of coronary angiographic images

The final diagnosis in coronary angiography has to be performed on the original images, therefore the lossless compression schemes play a key role in medical data base management and tele-diagnosis applications. This work proposes a wavelet based compression scheme that is able to operate in the lossless mode. The quantization module implements a new modality for the coding of the coefficient's significance map that is more effective than the classical zero-tree representation. The experimental results obtained on a set of 20 angiograms show that the algorithm outperforms with 0.38 bpp the embedded zero-tree coder combined with the lifting scheme, with 0.20 bpp the set partitioning coder and with 0.70 bpp the lossless JPEG. The scheme is a good candidate in applications like remote browsing through large image data sets and real-time archiving of coronary angiograms.

A fast convolution algorithm for biorthogonal wavelet image compression†

Symmetric filters and symmetric extension of image edges have been widely used in wavelet image compression. Since the filters are symmetric, it is possible to take advantage of the symmetric property to reduce the computational complexity for the filtering. In this paper, we present a fast convolution algorithm for the discrete wavelet transform (DWT) and the inverse DWT (IDWT) such that the transform time can be greatly reduced. Compared with regular convolution, the new algorithm can decrease the multiplication operations by nearly one half. Converted into real programming, it sped up the DWT and IDWT in our experiments by at least 12% and 55%, respectively. Incorporated with enhancing zerotree coding, the proposed algorithm results in a rapid and efficient coder. Experimental results showed that the coder is competitive with other high performance coders. The proposed convolution algorithm is also suitable for many types of wavelet‐based coding, including wavelet video coding.

Wavelet-based lossless compression scheme with progressive transmission capability

Lossless image compression with progressive transmission capabilities plays a key role in measurement applications, requiring quantitative analysis and involving large sets of images. This work proposes a wavelet-based compression scheme that is able to operate in the lossless mode. The quantization module implements a new technique for the coding of the wavelet coefficients that is more effective than the classical zerotree coding. The experimental results obtained on a set of multimodal medical images show that the proposed algorithm outperforms the embedded zerotree coder combined with the integer wavelet transform by 0.28 bpp, the set-partitioning coder by 0.1 bpp, and the lossless JPEG coder by 0.6 bpp. The scheme produces a losslessly compressed embedded data stream; hence, it supports progressive refinement of the decompressed images. Therefore, it is a good candidate for telematics applications requiring fast user interaction with the image data, retaining the option of lossless transmission and archiving of the images. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol 10: 76–85, 1999

Progressive lossless coding of medical images

The paper describes a procedure for lossless coding of medical images that uses a non-linear integer-to-integer wavelet transform generated by a lifting scheme and featuring progressive transmission capability. The quantization module implements a new modality for the coding of the wavelet coefficients that is more effective than the classical zerotree coding. Lossless image compression with progressive transmission capabilities plays a key role in medical image acquisition and handling. The contradictory requirements of exact data reconstruction possibility and of efficient and economic handling and transmission of large sets of images over large distances have to be met simultaneously. The experimental results, obtained on a set of 20 multimodal medical images, show that the algorithm outperforms other existing image lossless coding algorithms. Therefore it is a good candidate for telematics applications like teleradiology and PACS.

Wavelet zerotree image compression with packetization

We describe a combined wavelet zerotree coding and packetization method that provides excellent image compression and graceful degradation against packet erasure. For example, using 53-byte packets (48-byte payload), the algorithm compresses the 512/spl times/512 gray-scale Lena image to 0.2 b/pixel with a peak signal-to-noise ratio (PSNR) of 32.2 dB with no packet erasure, and 26.3 dB on average for 10% packets erased.

Biorthogonal and nonuniform lapped transforms for transform coding with reduced blocking and ringing artifacts

New lapped transforms are introduced. The lapped biorthononal transform (LBT) and hierarchical lapped biorthogonal transform (HLBT) are appropriate for image coding, and the modulated HLBT biorthogonal transform (MMLBT) and nonuniform modulated lapped biorthogonal transform (NMLBT) are appropriate for audio coding. The HLBT has a significantly lower computational complexity than the lapped orthogonal transform (LOT), essentially no blocking artifacts, and fewer ringing artifacts than the commonly used discrete cosine transform (DCT). The LBT and HLBT have transform coding gains that are typically between 0.5 and 1.2 dB higher than that of the DCT. Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LET and HLBT. The NMLBT has fewer ringing artifacts and better reproduction of transient sounds than the MLT, as shown in audio coding examples. Fast algorithms for both the HLBT and the NMLBT are presented.

A DCT-based embedded image coder using wavelet structure of DCT for very low bit rate video codec

This paper presents an efficient DCT-based embedded image coder designed for I(intra)-frame coding in a very low bit rate video codec. Motivated by the recognition that a DCT (discrete cosine transform) on N/spl times/N blocks of an image can be viewed as a wavelet decomposition with a uniform N/spl times/N-subband decomposition, the proposed coder rearranges the DCT transformed image into a 2-level wavelet pyramid structure and makes use of improved embedded zerotree coding. The proposed rearrangement structure is quite well coupled with a embedded zerotree coding. The resulting DCT-based embedded image coder shows a better rate-distortion performance than conventional H.263 and MPEG4 as well as EZW-style coders. Also, the performance of the proposed new coder is comparable to that of state-of-art still image compression methods. In addition, the embedded feature of the proposed coder makes it possible to encode the I-frame at the exactly chosen bit rate.

Joint thresholding and quantizer selection for transform image coding: entropy-constrained analysis and applications to baseline JPEG

Striving to maximize baseline (Joint Photographers Expert Group-JPEG) image quality without compromising compatibility of current JPEG decoders, we develop an image-adaptive JPEG encoding algorithm that jointly optimizes quantizer selection, coefficient "thresholding", and Huffman coding within a rate-distortion (R-D) framework. Practically speaking, our algorithm unifies two previous approaches to image-adaptive JPEG encoding: R-D optimized quantizer selection and R-D optimal thresholding. Conceptually speaking, our algorithm is a logical consequence of entropy-constrained vector quantization (ECVQ) design principles in the severely constrained instance of JPEG-compatible encoding. We explore both viewpoints: the practical, to concretely derive our algorithm, and the conceptual, to justify the claim that our algorithm approaches the best performance that a JPEG encoder can achieve. This performance includes significant objective peak signal-to-noise ratio (PSNR) improvement over previous work and at high rates gives results comparable to state-of-the-art image coders. For example, coding the Lena image at 1.0 b/pixel, our JPEG encoder achieves a PSNR performance of 39.6 dB that slightly exceeds the quoted PSNR results of Shapiro's wavelet-based zero-tree coder. Using a visually based distortion metric, we can achieve noticeable subjective improvement as well. Furthermore, our algorithm may be applied to other systems that use run-length encoding, including intraframe MPEG and subband or wavelet coding.

Stack-run image coding

We describe a new image coding approach in which a 4-ary arithmetic coder is used to represent significant coefficient values and the lengths of zero runs between coefficients. This algorithm works by raster scanning within subbands, and therefore involves much lower addressing complexity than other algorithms such as zerotree coding that require the creation and maintenance of lists of dependencies across different decomposition levels. Despite its simplicity, and the fact that these dependencies are not explicitly utilized, the algorithm presented here is competitive with the best enhancements of zerotree coding. In addition, it performs comparably with adaptive subband splitting approaches that involve much higher implementation complexity.