Design of IIR orthogonal wavelet filter banks using lifting scheme

The lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been adopted in the international standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement a class of infinite-impulse-response (IIR) orthogonal wavelet filter banks by using the lifting scheme with two lifting steps. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Then, the design of the proposed IIR orthogonal wavelet filter banks is discussed. The designed IIR orthogonal wavelet filter banks have approximately linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to the image compression, and then the coding performance of the proposed IIR filter banks is evaluated and compared with the conventional wavelet transforms.     

Optimization Design of Biorthogonal Wavelet Filter Banks for Extending JPEG 2000 Standard Part-2

A generic optimization design approach of biorthogonal wavelet filter banks (BWFB) for extending the JPEG 2000 standard part-2 is presented in this paper. This approach adopts Vaidyanathan optimal coding gain criterion to design the BWFB, and adopts peak signal-to-noise ratio (PSNR) as the criterion to optimize this BWFB. A functional relation between the general BWFB and their lifting scheme is derived in the first place with respect to one free variable, so that the optimization design of the BWFB is easier and more convenient. In addition, a general image model is formulated as a first-order Markov process driven by Gaussian white noise. It is taken as an input of two-channel filter banks which satisfy perfect reconstruction (PR) condition to realize subband coding for obtaining the optimal BWFB according to the Vaidyanathan optimal coding gain criterion. Finally, a new 9/7 BWFB with rational coefficients is proposed for extending the JPEG 2000 standard part-2, with PSNR of reconstructed images only 0.20 dB lower than standard CDF 9/7 BWFB for infrared thermal image compressions.     

Image coding using lapped biorthogonal transform

The wireless sensor network utilizes image compression algorithms like JPEG, JPEG2000, and SPIHT for image transmission with high coding efficiency. During compression, discrete cosine transform (DCT)–based JPEG has blocking artifacts at low bit-rates. But this effect is reduced by discrete wavelet transform (DWT)–based JPEG2000 and SPIHT algorithm but it possess high computational complexity. This paper proposes an efficient lapped biorthogonal transform (LBT)–based low-complexity zerotree codec (LZC), an entropy coder for image coding algorithm to achieve high compression. The LBT-LZC algorithm yields high compression, better visual quality with low computational complexity. The performance of the proposed method is compared with other popular coding schemes based on LBT, DCT and wavelet transforms. The simulation results reveal that the proposed algorithm reduces the blocking artifacts and achieves high compression. Besides, it is analyzed for noise resilience.     

Theory and factorization for a class of structurally regular biorthogonal filter banks

Regularity is a fundamental and desirable property of wavelets and perfect reconstruction filter banks (PRFBs). Among others, it dictates the smoothness of the wavelet basis and the rate of decay of the wavelet coefficients. This paper considers how regularity of a desired degree can be structurally imposed onto biorthogonal filter banks (BOFBs) so that they can be designed with exact regularity and fast convergence via unconstrained optimization. The considered design space is a useful class of M-channel causal finite-impulse response (FIR) BOFBs (having anticausal FIR inverses) that are characterized by the dyadic-based structure W(z)=I-UV/sup /spl dagger//+z/sup -1/UV/sup /spl dagger// for which U and V are M/spl times//spl gamma/ parameter matrices satisfying V/sup /spl dagger//U=I/sub /spl gamma//, 1/spl les//spl gamma//spl les/M, for any M/spl ges/2. Structural conditions for regularity are derived, where the Householder transform is found convenient. As a special case, a class of regular linear-phase BOFBs is considered by further imposing linear phase (LP) on the dyadic-based structure. In this way, an alternative and simplified parameterization of the biorthogonal linear-phase filter banks (GLBTs) is obtained, and the general theory of structural regularity is shown to simplify significantly. Regular BOFBs are designed according to the proposed theory and are evaluated using a transform-based image codec. They are found to provide better objective performance and improved perceptual quality of the decompressed images. Specifically, the blocking artifacts are reduced, and texture details are better preserved. For fingerprint images, the proposed biorthogonal transform codec outperforms the FBI scheme by 1-1.6 dB in PSNR.     

Vector Lifting Schemes for Stereo Image Coding

Many research efforts have been devoted to the improvement of stereo image coding techniques for storage or transmission. In this paper, we are mainly interested in lossy-to-lossless coding schemes for stereo images allowing progressive reconstruction. The most commonly used approaches for stereo compression are based on disparity compensation techniques. The basic principle involved in this technique first consists of estimating the disparity map. Then, one image is considered as a reference and the other is predicted in order to generate a residual image. In this paper, we propose a novel approach, based on vector lifting schemes (VLS), which offers the advantage of generating two compact multiresolution representations of the left and the right views. We present two versions of this new scheme. A theoretical analysis of the performance of the considered VLS is also conducted. Experimental results indicate a significant improvement using the proposed structures compared with conventional methods.     

Lossless Compression of Microarray Images Using Image-Dependent Finite-Context Models

The use of microarray expression data in state-of-the-art biology has been well established. The widespread adoption of this technology, coupled with the significant volume of data generated per experiment, in the form of images, has led to significant challenges in storage and query retrieval. In this paper, we present a lossless bitplane-based method for efficient compression of microarray images. This method is based on arithmetic coding driven by image-dependent multibitplane finite-context models. It produces an embedded bitstream that allows progressive, lossy-to-lossless decoding. We compare the compression efficiency of the proposed method with three image compression standards (JPEG2000, JPEG-LS, and JBIG) and also with the two most recent specialized methods for microarray image coding. The proposed method gives better results for all images of the test sets and confirms the effectiveness of bitplane-based methods and finite-context modeling for the lossless compression of microarray images.      

Biorthogonal and nonuniform lapped transforms for transform codingwith 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     

三维图像的任意形状ROI小波零块压缩编码算法

感兴趣区(ROI)编码是在JPEG2000中提出的一种重要的技术,然而JPEG2000算法却无法同时支持任意形状ROI和任意提升因子.本文提出了一种基于任意形状ROI和3D提升小波零块编码的3D体数据图像压缩算法.新的算法支持ROI内外从有损到无损的编码.一种简单的任意形状无损ROI掩码(Mask)生成方法被提出.考虑到3D子带的特点,我们采用改进的3DSPECK零块算法对变换后的系数进行编码.一些其它支持任意形状ROI编码的算法也在本文中被评估,试验显示本文算法具有更好的编码性能.     

基于双正交小波变换的航空图像压缩研究

提出一种基于提升方案的双正交小波变换结合SPIHT编码的图像压缩方法.小波提升方案是继多分辨分析之后,另一种非常有效的构造小波滤波器的方法,在双正交条件下按所需的小波性能自由构造双正交小波基,并能加快小波变换的执行速度.分析了应用提升方案构造双正交小波的算法,选用性能优良的双正交小波,结合SPIHT编码,进行图像压缩.实验表明,通过该方法进行图像压缩,图像重建质量较高.     

Matrix Factorizations for Parallel Integer Transformation

Integer mapping is critical for lossless source coding and has been used for multicomponent image compression in the new international image compression standard JPEG 2000. In this paper, starting from block factorizations for any nonsingular transform matrix, we introduce two types of parallel elementary reversible matrix (PERM) factorizations which are helpful for the parallelization of perfectly reversible integer transforms. With improved degree of parallelism and parallel performance, the cost of multiplications and additions can be, respectively, reduced to O(logN) and O(log²N) for an N by N transform matrix. These make PERM factorizations an effective means of developing parallel integer transforms for large matrices. We also present a scheme to block the matrix and allocate the load of processors for efficient transformation     

New family of lapped biorthogonal transform via lifting steps

By scaling all discrete cosine transform (DCT) intermediate output coefficients of the lapped transform and employing the type-II and type-IV DCT based on lifting steps, a new family of lapped biorthogonal transform is introduced, called the IntLBT. When all the elements with a floating point of each lifting matrix in the IntLBT are approximated by binary fractions, the IntLBT is implemented by a series of dyadic lifting steps and provides very fast, efficient in-place computation of the transform coefficients, and all internal nodes have finite precision. When each lifting step in the IntLBT is implemented using the same nonlinear operations as those used in the well known integer-to-integer wavelet transform, the IntLBT maps integers to integers, so it can express lossless image information. As an application of the novel IntLBT to lossy image compression, simulation results demonstrate that the IntLBT has significantly less blocking artefacts, higher peak signal-to-noise ratio, and better visual quality than the DCT. More importantly, the IntLBT's coding performance is approximately the same as that of the much more complex Cohen-Daubechies-Feauveau (CDF) 9/7-tap biorthogonal wavelet with floating-point coefficients, and in some cases even surpasses that of the CDF 9/7-tap biorthogonal wavelet.     

All phase biorthogonal transform and its application in JPEG-like image compression

This paper proposes new concepts of the all phase biorthogonal transform (APBT) and the dual biorthogonal basis vectors. In the light of all phase digital filtering theory, three kinds of all phase biorthogonal transforms based on the Walsh transform (WT), the discrete cosine transform (DCT) and the inverse discrete cosine transform (IDCT) are proposed. The matrices of APBT based on WT, DCT and IDCT are deduced, which can be used in image compression instead of the conventional DCT. Compared with DCT-based JPEG (DCT-JPEG) image compression algorithm at the same bit rates, the PSNR and visual quality of the reconstructed images using these transforms are approximate to DCT, outgoing DCT-JPEG at low bit rates especially. But the advantage is that the quantization table is simplified and the transform coefficients can be quantized uniformly. Therefore, the computing time becomes shorter and the hardware implementation easier.     

Stabilization and optimization of PLUS factorization and its application in image coding

A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stability theorem under no perturbation and analyze stability under perturbation. Furthermore, we obtain a closed-form formula for transform error, and use the formula to design an algorithm for optimal PLUS factorization. Then, we apply the PLUS factorization to image coding. The integer DCTs implemented with the optimal PLUS factorizations found by our algorithms outperform the integer DCT with expansion factors in terms of entropy. The optimal PLUS factorizations are superior to the lifting factorization in JPEG-XR. The experimental results agree with analytical results of PLUS factorization, and show superior performance of our algorithms in image coding.     

A class of regular biorthogonal linear-phase filterbanks: theory, structure, and application in image coding

This paper discusses a method of regularity imposition onto biorthogonal linear-phase M-band filterbanks using the lattice structure. A lifting structure is proposed for lattice matrix parameterization where regularity constraints can be imposed. The paper focuses on cases with analysis and synthesis filterbanks having up to two degrees of regularity. Necessary and sufficient conditions for regular filterbanks in terms of the filter impulse response, frequency response, scaling function, and wavelets are revisited and are derived in terms of the lattice matrices. This also leads to a constraint on the minimum filter length. Presented design examples are optimized for the purpose of image coding, i.e., the main objectives are coding gain and frequency selectivity. Simulation results from an image coding application also show that these transforms yield improvement in the perceptual quality in the reconstruction images. The approach has also been extended to the case of integer/rational lifting coefficients, which are desirable in many practical applications.     

JPEG2000小波变换器的VLSI结构设计

新一代静止图像压缩标准JPEG2000将离散小波变换(DWT)作为其核心变换技术,并推荐采用推举体制(lifting)快速算法来实现.空间组合推举体制算法(SCLA)大大降低了lifting的运算量.当选用9/7小波滤波器时,SCLA的乘法运算量只有lifting的7/12.本文提出了一种实现SCLA算法的VLSI结构,降低了基于lifting实现的运算量, 加快了变换的速度,减小了电路的规模.本文的二维正反小波变换器已经作为单独的IP核应用于我们目前正在开发的JPEG2000图像编解码芯片中.     

Coding gain and spatial localisation properties of discrete wavelettransform filters for image coding

The authors consider coding gain and spatial localisation properties of DWT filters for still image compression. Using a JPEG type quantisation and encoding method several images are compressed using a DWT implemented using various two-band subband filter sets. It is concluded that a relatively high coding gain (relative to a highly correlated source) is necessary, but not sufficient, for good image coding performance. Further, it is observed that low spatial width filters are desirable, particularly in regard to reduced ringing distortion. In terms of the trade-off between coding gain and spatial localisation, and in terms of actual coding performance, it is shown that biorthogonal filters can outperform orthogonal filters     

Error-resilient scalable compression based on distributed video coding

Distributed Video Coding (DVC) is a new paradigm for video compression based on the information theoretical results of Slepian–Wolf (SW) and Wyner–Ziv (WZ). In this work, a performance analysis of image and video coding schemes based on DVC is presented, addressing temporal, quality and spatial scalability. More specifically, conventional coding is used to obtain a base layer while WZ coding generates the enhancement layers. At the decoder, the base layer is used to construct Side Information (SI) for the DVC decoding process. Initially, we show that the scalable DVC approach is codec-independent, which means that it is independent from the method used to encode the base layer. Moreover, the influence of the base layer quality on the overall performance of the schemes is studied. Finally, evaluation of the proposed schemes is performed in both cases, with and without transmission errors. The simulation results show that scalable DVC has a lower compression efficiency than conventional scalable coding (i.e. scalable video coding and JPEG2000 for video and image, respectively) in error-free conditions. On the other hand, the DVC-based schemes show better error resilience as they outperform conventional scalable coding in error-prone conditions. More specifically, the Rate Distortion (RD) performance of the proposed schemes for image coding is compared with respect to Reed Solomon (RS) protected JPEG2000. While the latter exhibits a cliff effect as its performance dramatically decreases after a certain error rate, the performance of the DVC-based schemes decreases in a steady way with error rate increase.     

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.     

Two-Symbol FPGA Architecture for Fast Arithmetic Encoding in JPEG 2000

JPEG 2000 is one of the most popular image compression standards offering significant performance advantages over previous image standards. High computational complexity of the JPEG 2000 algorithms makes it necessary to employ methods that overcomes the bottlenecks of the system and hence an efficient solution is imperative. One such crucial algorithms in JPEG 2000 is arithmetic coding and is completely based on bit level operations. In this paper, an efficient hardware implementation of arithmetic coding is proposed which uses efficient pipelining and parallel processing for intermediate blocks. The idea is to provide a two-symbol coding engine, which is efficient in terms of performance, memory and hardware. This architecture is implemented in Verilog hardware definition language and synthesized using Altera field programmable gate array. The only memory unit used in this design is a FIFO (first in first out) of 256 bits to store the CX-D pairs at the input, which is negligible compared to the existing arithmetic coding hardware designs. The simulation and synthesis results show that the operating frequency of the proposed architecture is greater than 100 MHz and it achieves a throughput of 212 Msymbols/sec, which is double the throughput of conventional one-symbol implementation and enables at least 50% throughput increase compared to the existing two-symbol architectures.     

Optimal wavelet filter design for remote sensing image compression

A new approach for designing the Biorthogonal Wavelet Filter Bank （BWFB） for the purpose of image compression is presented in this letter. The approach is decomposed into two steps. First, an optimal filter bank is designed in theoretical sense based on Vaidyanathan＇s coding gain criterion in SubBand Coding （SBC） system. Then the above filter bank is optimized based on the criterion of Peak Signal-to-Noise Ratio （PSNR） in JPEG2000 image compression system, resulting in a BWFB in practical application sense. With the approach, a series of BWFB for a specific class of applications related to image compression, such as remote sensing images, can be fast designed. Here, new 5/3 BWFB and 9/7 BWFB are presented based on the above approach for the remote sensing image compression applications. Experiments show that the two filter banks are equally performed with respect to CDF 9/7 and LT 5/3 filter in JPEG2000 standard; at the same time, the coefficients and the lifting parameters of the lifting scheme are all rational, which bring the computational advantage, and the ease for VLSI implementation.