Image coding using translation invariant wavelet transforms withsymmetric extensions

In this correspondence, we address the problem of translation sensitivity of conventional wavelet transforms for two-dimensional (2-D) signals. We propose wavelet transform algorithms that achieve the following desirable properties simultaneously: (i) translation invariance, (ii) reduced edge effects, and (iii) size-limitedness. We apply this translation invariant biorthogonal wavelet transform with symmetric extensions to image coding applications with good results.     

Scalable image coding using reversible integer wavelet transforms

Reversible integer wavelet transforms allow both lossless and lossy decoding using a single bitstream. We present a new fully scalable image coder and investigate the lossless and lossy performance of these transforms in the proposed coder. The lossless compression performance of the presented method is comparable to JPEG-LS. The lossy performance is quite competitive with other efficient lossy compression methods.     

Progressive medical image coding using binary wavelet transforms

In this paper, a new algorithm for progressive medical image coding is presented. An 8-bit gray scale image is divided into eight binary bit-planes, and then, binary wavelet transform is performed on each bit-plane to extract the three-level multi-resolution binary wavelet transformed images. Starting from the most significant bit-plane, each bit-plane is encoded using quadtree-based partitioning scheme to exploit the energy concentration in the high-frequency subbands. Experiments are conducted on ultrasound, MRI and CT images to prove the effectiveness of the proposed algorithm. The results show a significant improvement in terms of bit-rate for the required peak signal-to-noise ratio and correlation coefficient as compared to the existing state-of-art progressive image coding methods.     

Image coding using wavelet transform

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission.     

Image coding using entropy-constrained residual vector quantization

An entropy-constrained residual vector quantization design algorithm is used to design codebooks for image coding. Entropy-constrained residual vector quantization has several important advantages. It can outperform entropy-constrained vector quantization in terms of rate-distortion performance, memory, and computation requirements. It can also be used to design vector quantizers with relatively large vector sizes and high output rates. Experimental results indicate that good image reproduction quality can be achieved at relatively low bit rates. For example, a peak signal-to-noise ratio of 30.09 dB is obtained for the 512x512 LENA image at a bit rate of 0.145 b/p.     

Three-dimensional wavelet transform video coding using symmetriccodebook vector quantization

A new vector quantizer codebook design for video compression is described. This uses the notion that symmetries in the data, which are seldom captured exactly in any training dataset, are important perceptually and lead to a more robust codebook. The method is illustrated using three-dimensional (3-D) wavelet transformed video sequences.     

Image subband coding using context-based classification andadaptive quantization

Adaptive compression methods have been a key component of many proposed subband (or wavelet) image coding techniques. This paper deals with a particular type of adaptive subband image coding where we focus on the image coder's ability to adjust itself "on the fly" to the spatially varying statistical nature of image contents. This backward adaptation is distinguished from more frequently used forward adaptation in that forward adaptation selects the best operating parameters from a predesigned set and thus uses considerable amount of side information in order for the encoder and the decoder to operate with the same parameters. Specifically, we present backward adaptive quantization using a new context-based classification technique which classifies each subband coefficient based on the surrounding quantized coefficients. We couple this classification with online parametric adaptation of the quantizer applied to each class. A simple uniform threshold quantizer is employed as the baseline quantizer for which adaptation is achieved. Our subband image coder based on the proposed adaptive classification quantization idea exhibits excellent rate-distortion performance, in particular at very low rates. For popular test images, it is comparable or superior to most of the state-of-the-art coders in the literature.     

Image coding using vector quantization: a review

A review of vector quantization techniques used for encoding digital images is presented. First, the concept of vector quantization is introduced, then its application to digital images is explained. Spatial, predictive, transform, hybrid, binary, and subband vector quantizers are reviewed. The emphasis is on the usefulness of the vector quantization when it is combined with conventional image coding techniques, or when it is used in different domains     

Image coding using robust quantization for noisy digitaltransmission

A robust quantizer is developed for encoding memoryless sources and transmission over the binary symmetric channel (BSC). The system combines channel optimized scalar quantization (COSQ) with all-pass filtering, the latter performed using a binary phase-scrambling/descrambling method. Applied to a broad class of sources, the robust quantizer achieves the same performance as the Gaussian COSQ for the memoryless Gaussian source. This quantizer is used in image coding for transmission over a BSC. The peak signal-to-noise ratio (PSNR) performance degrades gracefully as the channel bit error rate increases.     

Space-frequency quantization for wavelet image coding

A new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree-structured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out tree-structured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all nonzeroed coefficients), and we formalize the problem of optimizing their joint application. We develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive, often outperforming the very best coding algorithms in the literature.     

Image coding using dual-tree discrete wavelet transform

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. Three methods for sparsifying DDWT coefficients, i.e., matching pursuit, basis pursuit, and noise shaping, are compared. We found that noise shaping achieves the best nonlinear approximation efficiency with the lowest computational complexity. The interscale, intersubband, and intrasubband dependency among the DDWT coefficients are analyzed. Three subband coding methods, i.e., SPIHT, EBCOT, and TCE, are evaluated for coding DDWT coefficients. Experimental results show that TCE has the best performance. In spite of the redundancy of the transform, our DDWT _ TCE scheme outperforms JPEG2000 up to 0.70 dB at low bit rates and is comparable to JPEG2000 at high bit rates. The DDWT _TCE scheme also outperforms two other image coders that are based on directional filter banks. To further improve coding efficiency, we extend the DDWT to an anisotropic dual-tree discrete wavelet packets (ADDWP), which incorporates adaptive and anisotropic decomposition into DDWT. The ADDWP subbands are coded with TCE coder. Experimental results show that ADDWP _ TCE provides up to 1.47 dB improvement over the DDWT _TCE scheme, outperforming JPEG2000 up to 2.00 dB. Reconstructed images of our coding schemes are visually more appealing compared with DWT-based coding schemes thanks to the directionality of wavelets.     

Image coding using wavelet transform and classified vectorquantisation

The wavelet transform, which provides a multiresolution representation of images, has been widely used in image compression. A new image coding scheme using the wavelet transform and classified vector quantisation is presented. The input image is first decomposed into a hierarchy of three layers containing ten subimages by the discrete wavelet transform. The lowest resolution low frequency subimage is scalar quantised with 8 bits/pixel. The high frequency subimages are compressed by classified vector quantisation to utilise the crosscorrelation among different resolutions while reducing the edge distortion and computational complexity. Vectors are constructed by combining the corresponding wavelet coefficients of different resolutions in the same orientation and classified according to the magnitude and the position of wavelet transform coefficients. Simulation results show that the proposed scheme has a better performance than those utilising current scalar or vector quantisation schemes     

Hierarchical quantization indexing for wavelet and wavelet packet image coding

In this paper, we introduce the quantization index hierarchy, which is used for efficient coding of quantized wavelet and wavelet packet coefficients. A hierarchical classification map is defined in each wavelet subband, which describes the quantized data through a series of index classes. Going from bottom to the top of the tree, neighboring coefficients are combined to form classes that represent some statistics of the quantization indices of these coefficients. Higher levels of the tree are constructed iteratively by repeating this class assignment to partition the coefficients into larger subsets. The class assignments are optimized using a rate-distortion cost analysis. The optimized tree is coded hierarchically from top to bottom by coding the class membership information at each level of the tree. Context-adaptive arithmetic coding is used to improve coding efficiency. The developed algorithm produces PSNR results that are better than the state-of-art wavelet-based and wavelet packet-based coders in literature.     

The coding gain of multiplexed wavelet transforms

Evangelista (1994, 1993) introduced the multiplexed wavelet transform (MWT) and pointed out its potential applications to the analysis, synthesis, processing and coding of pseudo-periodic signals such as voiced speech and music. Coders based on the MWT have been shown to outperform the conventional subband coders when a reliable pitch parameter can be extracted from data. In this paper, we investigate the effects of uniform quantization of the MWT coefficients. We compare the performance of the new coders with that of WT, block-DCT, and KLT coders in terms of the coding gain achieved when optimal bit allocation schemes are adopted     

Image compression using bit-plane coding of wavelet coefficients

The authors propose new simple image coder based on a discrete wavelet transform (DWT). The DWT coefficients are coded in bit-planes. They use an improved version of the JBIG bi-level image compression method to code the DWT coefficient bit-planes. The experimental results are shown, both in distortion measurement and visual comparison, and are very promising     

Nonlinear wavelet transforms for image coding via lifting

We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear wavelet transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels. Preliminary compression results for model and real-world images demonstrate the promise of our techniques.     

Structured vector quantization using linear transforms

This paper presents novel structured vector quantization (VQ) techniques characterized by the use of linear transformations for the input VQ. The first technique is called the affine transformations VQ, in which the quantized vector is formed by adding the transformed outputs of a multistage codebook rather than just adding the outputs of the stages as in regular multistage vector quantization (MSVQ). The name of the VQ technique comes from the fact that in the two-stage case, the quantized vector is obtained as the result of an affine transformation. This technique can be viewed as a generalized form of MSVQ. If the transformations are constrained to be the identity transformation, this technique becomes identical to the regular MSVQ. The transformations in the introduced technique are selected from a family of linear transformations, represented by a codebook of matrices. In order to I reduce the memory required for storing the matrices, the paper discusses a second technique called scaled rotation matrices VQ, where matrices are constrained to be scaled rotation matrices. Since rotation matrices can be stored by just storing the corresponding rotation angles, this approach enables efficient storage of linear transforms. The design algorithms are based on joint optimization of the linear transformation and the stage codebooks. Experimental results based on speech spectrum quantization show that the proposed VQ techniques outperform the MSVQ of the same bit rate.