The application of multiwavelet filterbanks to image processing

Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional (1-D) signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.     

Image compression through embedded multiwavelet transform coding

In this paper, multiwavelets are considered in the context of image compression and two orthonormal multiwavelet bases are experimented, each used in connection with its proper prefilter. For evaluating the effectiveness of multiwavelet transform for coding images at low bit-rates, an efficient embedded coding of multiwavelet coefficients has been realized. The performance of this multiwavelet-based coder is compared with the results obtained for scalar wavelets.     

小波变换编码及其在军事图像上的应用

提出了一种军事图像压缩的新方法,在嵌入式零树小波(EZW)算法基础上引入提升方案和整数变换以降低算法复杂度,在编码前对系数按重要性进行排序并对低频区域的系数的符号进行改变.实验结果表明,将该算法用于军事图像压缩无论在主观效果还是在峰值信噪比方面都取得了满意的效果.     

Hadamard transform image coding

The introduction of the fast Fourier transform algorithm has led to the development of the Fourier transform image coding technique whereby the two-dimensional Fourier transform of an image is transmitted over a channel rather than the image itself. This devlopement has further led to a related image coding technique in which an image is transformed by a Hadamard matrix operator. The Hadamard matrix is a square array of plus and minus ones whose rows and columns are orthogonal to one another. A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed. Since only real number additions and subtractions are required with the Hadamard transform, an order of magnitude speed advantage is possible compared to the complex number Fourier transform. Transmitting the Hadamard transform of an image rather than the spatial representation of the image provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.     

Digital image coding using legendre transform

Image coding can be implemented through DPCM, transform, hybrid, or segmentation coding techniques. Some transform coding techniques, such as cosine and Hadamard, have been exhaustively analyzed and evaluated, while others, such as Legendre, have not. This paper introduces the use of Legendre transform in image coding. The transform matrix for different block sizes is calculated, the fast algorithm is derived, and the performance is evaluated through both mean square error and subjective quality. The results obtained have indicated that the system performance is comparable with that of optimum KLT and cosine transforms; moreover, it is simpler in implementation.     

Vector-scalar classification for transform image coding

This paper introduces vector-scalar classification (VSC) for discrete cosine transform (DCT) coding of images. Two main characteristics of VSC differentiate it from previously proposed classification methods. First, pattern classification is effectively performed in the energy domain of the DCT subvectors using vector quantization. Second, the subvectors, instead of the DCT vectors, are mapped into a prescribed number of classes according to a pattern-to-class link established by scalar quantization. Simulation results demonstrate that the DCT coding systems based on VSC are superior to the other proposed DCT coding systems and are competitive compared to the best subband and wavelet coding systems reported in the literature.     

Extended lapped transform in image coding

A modulated lapped transform with extended overlap (ELT) is investigated in image coding with the objective of verifying its potential to replace the discrete cosine transform (DCT) in specific applications. Some of the criteria utilized for the performance comparison are reconstructed image quality (both objective and subjective), reduction of blocking artifacts, robustness against transmission errors, and filtering (for scalability). Also, a fast implementation algorithm for finite-length-signals using symmetric extensions is developed specially for the ELT with overlap factor 2 (ELT-2). This comparison shows that ELT-2 is superior to both DCT and the lapped orthogonal transform (LOT).     

Maximally smooth image recovery in transform coding

The authors consider the reconstruction of images from partial coefficients in block transform coders and its application to packet loss recovery in image transmission over asynchronous transfer mode (ATM) networks. The proposed algorithm uses the smoothness property of common image signals and produces a maximally smooth image among all those with the same coefficients and boundary conditions. It recovers each damaged block by minimizing the intersample variation within the block and across the block boundary. The optimal solution is achievable through two linear transformations, where the transform matrices depend on the loss pattern and can be calculated in advance. The reconstruction of contiguously damaged blocks is accomplished iteratively using the previous solution as the boundary conditions in each new step. This technique is applicable to any unitary block-transform and is effective for recovering the DC and low-frequency coefficients. When applied to still image coders using the discrete cosine transform (DCT), high quality images are reconstructed in the absence of many DC and low-frequency coefficients over spatially adjacent blocks. When the damaged blocks are isolated by block interleaving, satisfactory results have been obtained even when all the coefficients are missing     

Curved wavelet transform for image coding.

The conventional two-dimensional wavelet transform used in existing image coders is usually performed through one-dimensional (1-D) filtering in the vertical and horizontal directions, which cannot efficiently represent edges and lines in images. The curved wavelet transform presented in this paper is carried out by applying 1-D filters along curves, rather than being restricted to vertical and horizontal straight lines. The curves are determined based on image content and are usually parallel to edges and lines in the image to be coded. The pixels along these curves can be well represented by a small number of wavelet coefficients. The curved wavelet transform is used to construct a new image coder. The code-stream syntax of the new coder is the same as that of JPEG2000, except that a new marker segment is added to the tile headers. Results of image coding and subjective quality assessment show that the new image coder performs better than, or as well as, JPEG2000. It is particularly efficient for images that contain sharp edges and can provide a PSNR gain of up to 1.67 dB for natural images compared with JPEG2000.     

Predictive subband image coding with wavelet transform

Wavelet transform can decompose images into various multiresolution subbands. In these subbands the correlation exists. A novel technique for image coding by taking advantage of the correlation is addressed. It is based on predictive edge detection from the LL band of the lowest resolution level to predict the edge in the LH, HL and HH bands in the higher resolution level. If the coefficient is predicted as an edge it is preserved; otherwise, it is discarded. In the decoder, the location of the preserved coefficients can also be found as in the encoder. Therefore, no overhead is needed. Instead of complex vector quantization, which is commonly used in subband image coding for high compression ratio, simple scalar quantization is used to code the remaining coefficients and achieves very good results.     

Analysis of low bit rate image transform coding

Calculations based on high-resolution quantizations prove that the distortion rate D(R¯) of an image transform coding is proportional to 2^-2R when R¯ is large enough. In wavelet and block cosine bases, we show that if R¯<1 bit/pixel, then D(R¯) varies like R¯^1-2γ, where γ remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. At low bit rates, we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors     

A new approach to reduce the `blocking effect' of transform coding[image coding]

A combined-transform coding (CTC) scheme to reduce the blocking effect of conventional block transform coding and hence to improve the subjective performance is presented. The scheme is described, and its information-theoretic properties are discussed. Computer simulation results for a chest X-ray image are presented. The CTC scheme, the JPEG baseline scheme, and the conventional discrete Walsh-Hadamard transform (DWHT) are compared to demonstrate the performance improvement for the CTC scheme. The advantages of the CTC scheme include no ringing effect as there is no error propagation across the boundary, no additional computation, and distortion always held within a certain level     

Wavelet transform image coding using lattice vector quantisation

A novel method for the efficient coding of image wavelet coefficients using zerotree multistage lattice vector quantisation is presented. This method achieves high compression ratios with good picture quality, maintaining a very simple implementation. Simulation results demonstrate that the coding performance of this algorithm favourably compares to some of the best reported image compression results     

Improvement on image transform coding by reducing interblockcorrelation

We try to improve transform coding efficiency by alleviating the interblock correlation due to the small size of the block. The proposed method needs minor modification from conventional transform coding techniques such as JPEG, and reduces the information loss in the coding procedure for a given bit rate. Simulation results demonstrate that the method drastically diminishes the blocking effects and enhances the subjective visual quality compared with such existing algorithms as JPEG and LOT.     

Adaptive cosine transform image coding with constant blockdistortion

An adaptive block discrete-cosine transform (DCT) coding scheme is implemented with the same average distortion designated for each block. This constant distortion designation not only has perceptual advantages, but also allows the rate to vary, adjusting to the changing spectral characteristics among the blocks. The successful execution of this scheme requires a different spectral estimate for each block. To keep overhead and computation within limits, a novel technique is introduced by which a two-dimensional block spectrum is characterized by a one-dimensional autoregressive model. Simulations with images of natural scenes and medical radiology provide reconstructions with nearly uniform block distortion and very high visual and measurable quality at low rates     

The discrete modal transform and its application to lossy image compression

This paper introduces the discrete modal transform (DMT), a 1D and 2D discrete, non-separable transform for signal processing, which, in the mathematical sense, is a generalization of the well-known discrete cosine transform (DCT). A 3D deformable surface model is used to represent the image intensity and the introduced discrete transform is a by-product of the explicit surface deformation governing equations. The properties of the proposed transform are similar to those of the DCT. To illustrate these properties, the proposed transform is applied to lossy image compression and the obtained results are compared to those of a DCT-based compression scheme. Experimental results show that DMT, which includes an embedded compression ratio selection mechanism, has excellent energy compaction properties and achieves comparable compression results to DCT at low compression ratios, while being in general better than DCT at high compression ratios.     

块重叠小波变换及其在音频编码中的应用

小波变换是信源编码技术的重要数学工具。然而,由于基于块的小波变换的基函数在块边界处的不连续性,导致解码信号在块边界存在“块效应”问题。本文采用块重叠小波变换的方法,利用变换基函数在块边界的连续性,消除了解码信号的“块效应”问题。基于块重叠小波包变换技术,设计了一个音频编码器,验证了上述方法的有效性。     

Adaptive directional lifting-based wavelet transform for image coding.

We present a novel 2-D wavelet transform scheme of adaptive directional lifting (ADL) in image coding. Instead of alternately applying horizontal and vertical lifting, as in present practice, ADL performs lifting-based prediction in local windows in the direction of high pixel correlation. Hence, it adapts far better to the image orientation features in local windows. The ADL transform is achieved by existing 1-D wavelets and is seamlessly integrated into the global wavelet transform. The predicting and updating signals of ADL can be derived even at the fractional pixel precision level to achieve high directional resolution, while still maintaining perfect reconstruction. To enhance the ADL performance, a rate-distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features. Experimental results show that the proposed ADL-based image coding technique outperforms JPEG 2000 in both PSNR and visual quality, with the improvement up to 2.0 dB on images with rich orientation features.     

Peak transform for efficient image representation and coding.

In this work, we introduce a nonlinear geometric transform, called peak transform (PT), for efficient image representation and coding. The proposed PT is able to convert high-frequency signals into low-frequency ones, making them much easier to be compressed. Coupled with wavelet transform and subband decomposition, the PT is able to significantly reduce signal energy in high-frequency subbands and achieve a significant transform coding gain. This has important applications in efficient data representation and compression. To maximize the transform coding gain, we develop a dynamic programming solution for optimum PT design. Based on PT, we design an image encoder, called the PT encoder, for efficient image compression. Our extensive experimental results demonstrate that, in wavelet-based subband decomposition, the signal energy in high-frequency subbands can be reduced by up to 60% if a PT is applied. The PT image encoder outperforms state-of-the-art JPEG2000 and H.264 (INTRA) encoders by up to 2-3 dB in peak signal-to-noise ratio (PSNR), especially for images with a significant amount of high-frequency components. Our experimental results also show that the proposed PT is able to efficiently capture and preserve high-frequency image features (e.g., edges) and yields significantly improved visual quality. We believe that the concept explored in this work, designing a nonlinear transform to convert hard-to-compress signals into easy ones, is very useful. We hope this work would motivate more research work along this direction.     

Optimal block cosine transform image coding for noisy channels

A method is presented for the joint source-channel coding optimization of a scheme based on the two-dimensional block cosine transform when the output of the encoder is to be transmitted via a memoryless binary symmetric channel. The authors' approach involves an iterative algorithm for the design of the quantizers (in the presence of channel errors) used for encoding the transform coefficients. This algorithm produces a set of locally optimum (in the mean-squared error sense) quantizers and the corresponding binary codeword assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, the authors have used an algorithm based on the steepest descent method, which, under certain convexity conditions on the performance of the channel-optimized quantizers, yields the optimal bit allocation. Simulation results for the performance of this locally optimum system over noisy channels have been obtained, and appropriate comparisons with a reference system designed for no channel errors have been made. It is shown that substantial performance improvements can be obtained by using this scheme. Furthermore, theoretically predicted results and rate distortion-theoretic bounds for an assumed two-dimensional image model are provided