Subband Image Coding Research Articles

Sub-band coding of hexagonal images

According to the circle-packing theorem, the packing efficiency of a hexagonal lattice is higher than an equivalent square tessellation. Consequently, in several contexts, hexagonally sampled images compared to their Cartesian counterparts are better at preserving information content. In this paper, novel mapping techniques alongside the wavelet compression scheme are presented for hexagonal images. Specifically, we introduce two tree-based coding schemes, referred to as SBHex (spirally-mapped branch-coding for hexagonal images) and BBHex (breadth-first block-coding for hexagonal images). Both of these coding schemes respect the geometry of the hexagonal lattice and yield better compression results. Our empirical results show that the proposed algorithms for hexagonal images produce better reconstruction quality at low bits per pixel representations compared to the tree-based coding counterparts for the Cartesian grid.

A Novel Strong Decorrelation Approach for Image Subband Coding Using Polynomial EVD Algorithms

Subband coding is a popular technique to achieve multichannel data compression and efficient data transmission in image and video communications. In this paper, we focus on designing a data-dependent image subband coder which divides the image into strongly (total) decorrelated and spectrally majorized subbands, which seeks to reduce the redundancy to achieve better compression and efficient transmission. To achieve strong decorrelation and spectral majorization between the subbands, we adopt a set of new iterative polynomial eigenvalue decomposition (PEVD) algorithms: sequential matrix diagonalization (SMD) and maximum element sequential matrix diagonalization (ME-SMD). Using this SMD-based PEVD approach, we design the data dependent subband coder (DDSC) for image subband coding. We compare the performance of the proposed SMD/ME-SMD algorithms with the existing DDSC methods like SBR2, SBR2C, K–L transform (KLT) coder and data independent subband coder (DISC)-based discrete wavelet transform (DWT) technique. To measure the performance, we use the parameters like coding gain, correlation coefficient, MSE (mean square error) and peak signal-to-noise ratio (PSNR). The presented simulation results for standard images in the absence of quantization show that the proposed SMD-based PEVD technique performs far better than the existing techniques.

Optimum Space-Frequency Partition in Subband Image Coding with Human Visual Sensitivity and Region-of-Interest

Optimum Space-Frequency Partition in Subband Image Coding with Human Visual Sensitivity and Region-of-Interest

Optimum Frequency Band Partition Based on Kurtosis in Subband Image Coding

Optimum Frequency Band Partition Based on Kurtosis in Subband Image Coding

画像のサブバンド符号化における符号化レートに応じた最適帯域分割

In subband image coding, the optimum frequency band partition was previously proposed on the basis of the power spectrum of an input image. However, the partition pattern on the 2-D frequency domain was invariable when the bit rate changed. Therefore, a new optimum frequency band partition has been developed that can determine both the partition pattern on the 2-D frequency domain and the combination of quantizers with subband signals for the given bit rate. The experimental results show that the proposed method improved the coding performances at the lower bit rate compared with the conventional method.

Perceptually tuned subband coder for JPEG

This paper presents a perceptually tuned subband image coder, which selectively operates on the subbands of an image to achieve good compression ratio. The proposed encoder divides an image into 8 × 8 sub-images and subsequently decomposes each sub-image into four subbands. A just noticeable distortion (JND) model is employed to remove all the perceptually insignificant subbands from the sub-images. The remaining subbands are processed by the subband discrete cosine transform (SBDCT). This reduces the computational cost of the SBDCT without introducing perceptible distortion. To further reduce the perceptual redundancy in the image, an image-dependent quantization matrix is computed from the JND profile of the image. Our simulation results indicate that our proposed encoder outperforms the JPEG baseline coder at bit rates from 0.25 to 0.9 bpp.

Fractional Fourier domain analysis of cyclic multirate signal processing

The cyclic filter banks, which are used widely in the image subband coding, refer to signal processing on the finite field. This study investigates the fractional Fourier domain (FRFD) analysis of cyclic multirate systems based on the fractional circular convolution and chirp period. The proposed theorems include the fractional Fourier domain analysis of cyclic decimation and cyclic interpolation, the noble identities of cyclic decimation and cyclic interpolation in the FRFD, the polyphase representation of cyclic signal in the FRFD, and the perfect reconstruction condition for the cyclic filter banks in the FRFD. Furthermore, this paper proposes the design methods for perfect reconstruction cyclic filter bank and cyclic filter bank with chirp modulation in the FRFD. The proposed theorems extend the multirate signal processing in the FRFD, which also advance the applications of the theorems of filter bank in the FRFD on the finite signal field, such as digital image processing. At last, the proposed design methods for the cyclic filter banks in the FRFD are validated by simulations.

A COVQ-based image coder for channels with bit errors and erasures

We illustrate how channel optimized vector quantization (COVQ) can be used for channels with both bit-errors and bit-erasures. First, a memoryless channel model is presented, and the performance of COVQ's trained for this channel is evaluated for an i.i.d. Gaussian source. Then, the new method is applied in implementing an error-robust sub-band image coder, and we present image results that illustrate the resulting performance. Our experiments show that the new approach is able to outperform a traditional scheme based on separate source and channel coding.

Entropy-Based Distortion Measure and Bit Allocation for Wavelet Image Compression

Quality criteria for image coding are often based on mean square error. However, this is not always a relevant measure of visual quality at low bit rates. Here, we investigate the properties of a distortion measure based on the conditional differential entropy of the input signal given its quantized value. The proposed measure appears to be a correct representation of the amount of information lost by quantization. An adaptive bit allocation algorithm is proposed in order to take advantage of this criterion. Experimental results illustrate the behavior of the proposed distortion measure and exhibit interesting visual properties for low bit-rate subband image coding.

Adaptive modulated wavelet subband image coding

High quality, embedded, variable rate image compression can be achieved by decomposing an image into subbands of different sizes, modeling with one significant AM–FM component as well as encoding with a distinct procedure for each subband. In this paper, an adaptive subband decomposition using the modulated wavelet packet transform is proposed, where the adaptation of modulating frequencies is based on the energy spectral density in a resolution-recursive framework; and, each subband can be well represented by the modulated wavelets. An extension of SPIHT algorithm that is needed for encoding the complex-valued modulated wavelet coefficients is also presented. Experimental results show that the modulated wavelet subband image coding is preferable to both the wavelet coding and the JPEG standard.

Quadtree-based classification in subband image coding

Classification of blocks of subband samples according to their energy and variable bit allocation within the subsequent classes has demonstrated considerable gains in coding efficiency. The gains due to classification increase as smaller blocks are used; however, this increases the overheads for transmitting the classification information. In this paper, a quadtree based method is proposed. This method allows for more efficient classification by using variable-sized blocks in order to maximize the classification gain, while maintaining a limit on the classification overheads. This method is applied for subband coding of images and the results indicate that it performs better than the other methods currently available in the literature.

Optimum partition of two‐dimensional frequency band with human visual sensitivity for subband image coding

AbstractThis paper proposes a method of optimizing the partition of a two‐dimensional frequency band so that high‐quality reconstructed images are obtained by subband image coding. This partitioning is derived by minimizing the weighted quantization noise power with human visual sensitivity. To simplify the coding system, the structure of the filter bank is analyzed. The band partition parameters which makes the filter bank more efficient are selected, based on experimental results for actual images. The quality of images reconstructed by the proposed method is evaluated by using the relationship between the weighted quantized noise power and their entropy. The proposed method is subjectively evaluated by comparing it with a nonweighted method and the DCT method. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(3): 96–110, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1198

画像符号化用電力相補特性２チャネル直線位相偶数次ＩＩＲフィルタバンク

This paper presents a method for designing a 6th-order two-channel linear-phase IIR filter bank with quasi-power complementary characteristics for image subband coding. The lowpass filter is specified to have a double or quadruple zero at ω = π and is designed with weighted equiripple approximation based on the formulation of an eigen-value problem. A design example of an image subband coding system using a three-stage octave division filter bank with rounded integer analysis output signals has shown to have a pseudo perfect reconstruction image “Lena” with a PSNR as highas 55.8 dB. The coding performance (PSNR versus bit rate) using bit plane arithmetic coding was nearly equal to that of 5th-order IIR filter banks and superior to 9 / 7 FIR filter banks.

Design of two-channel perfect-reconstruction linear-phase finite-duration impulse response filter banks for subband image coding by the genetic algorithm approach

In this paper, a powerful approach is proposed for the design of two-dimensional two-channel perfect-reconstruction finite-duration impulse response filter banks employing diamond-shaped linear-phase filters. When one of the analysis filter pair is properly designed, the condition of perfect reconstruction is formulated in a spatial-domain constraint equation for designing the other. The method is based on minimizing the integrated square error for the frequency response over the pass band and stop band while imposing the spatial-domain constraint. One numerical design example is given to demonstrate the perfect reconstruction for the proposed system.

Design of two-channel perfect-reconstruction linear-phase finite-duration impulse response filter banks for subband image coding by the genetic algorithm approach

In this paper, a powerful approach is proposed for the design of two-dimensional two-channel perfect-reconstruction finite-duration impulse response filter banks employing diamond-shaped linear-phase filters. When one of the analysis filter pair is properly designed, the condition of perfect reconstruction is formulated in a spatial-domain constraint equation for designing the other. The method is based on minimizing the integrated square error for the frequency response over the pass band and stop band while imposing the spatial-domain constraint. One numerical design example is given to demonstrate the perfect reconstruction for the proposed system.

Line-based, reduced memory, wavelet image compression

This paper addresses the problem of low memory wavelet image compression. While wavelet or subband coding of images has been shown to be superior to more traditional transform coding techniques, little attention has been paid until recently to the important issue of whether both the wavelet transforms and the subsequent coding can be implemented in low memory without significant loss in performance. We present a complete system to perform low memory wavelet image coding. Our approach is "line-based" in that the images are read line by line and only the minimum required number of lines is kept in memory. There are two main contributions of our work. First, we introduce a line-based approach for the implementation of the wavelet transform, which yields the same results as a "normal" implementation, but where, unlike prior work, we address memory issues arising from the need to synchronize encoder and decoder. Second, we propose a novel context-based encoder which requires no global information and stores only a local set of wavelet coefficients. This low memory coder achieves performance comparable to state of the art coders at a fraction of their memory utilization.

Removal of Grid-Pattern Noise Introduced by M -Channel Subband Image Coding

Amethod is proposed for reducing grid-pattern noise introduced by low bit-rate coding of images using integer-modulated filter banks. The noise level can be reduced significantly by applying a predictive subband coefficient compensation algorithm in the iterative synthesis filtering stage. Simulation results show the improvement in visual quality and a decrease in mean square error values of about 2 to 5. The coefficient compensation algorithm is suitable for real-time implementation since it is computationally simple and uses only integer operations.

Generalized unequal length lapped orthogonal transform for subband image coding

Generalized linear phase lapped orthogonal transforms with unequal length basis functions (GULLOTs) are considered. The length of each basis of the proposed GULLOT can be different from each other, whereas all the bases of the conventional GenLOT are of equal length. In general, for image coding application, the long basis for a low-frequency band and the short basis for a high-frequency one are desirable to reduce the blocking and the ringing artifact simultaneously. Therefore, the GULLOT is suitable especially for a subband image coding. In order to apply the GULLOT to a subband image coding, we also investigate the size-limited structure to process the finite length signal, which is important in practice. Finally, some design and image coding examples are shown to confirm the validity of the proposed GULLOT.

Optimal subband coders of quantized multidimensional signals

A new general method is presented for the analysis of the effects of quantization and transmission noise in subband filter-bank multidimensional signal and image coders. Using general statistical noise characterization, the filter banks are obtained, which are optimal in the sense of minimizing the variance of the difference of the reconstructed signal from the original. It is shown that these are not identical to those achieving perfect reconstruction in lossless coding. A general method is described for the optimal selection of the synthesis filters if the analysis filters and quantizers are given. Assuming the use of these optimal synthesis filters, a method is then developed for the determination of the optimal analysis filters and the optimal bit-allocation to the subbands. The effects of quantization on perfect reconstruction filter-banks are analyzed next, and an explicit expression is determined for the quantizer noise-to-signal ratio for such banks. Given arbitrary quantizers, the analysis filters which are optimal in the sense of minimizing the output noise power are obtained. Finally, the jointly optimal selection is determined for the analysis filters and the bit allocations of the subbands. It is seen that this selection is identical to that determined for the theoretically optimal filter-banks.

An integrated framework for adaptive subband image coding

Previous work on filter banks and related expansions has revealed an interesting insight: different filter bank trees can be regarded as different ways of constructing orthonormal bases for linear signal expansion. In particular, fast algorithms for finding best bases in an operational rate-distortion (R/D) sense have been successfully used in image coding. Independently of this work, other research has also explored the design of filter banks that optimize energy compaction for a single signal or a class of signals. In this paper, we integrate these two different but complementary approaches to best-basis design and propose a coding paradigm in which subband filters, tree structure, and quantizers are chosen to optimize the R/D performance. These coder attributes represent side information. They are selected from a codebook designed off-line from training data, using R/D as the design criterion. This approach provides a rational framework in which to explore alternatives to empirical design of filter banks, quantizers, and other coding parameters. The on-line coding algorithm is a relatively simple extension of current R/D-optimal coding algorithms that operate with fixed filter banks and empirically designed quantizer codebooks. In particular, it is shown that selection of the best adapted filter bank from the codebook is computationally elementary.