Lattice structure for arbitrary-length oversampled linear phase paraunitary filter bank with unequal numbers of symmetric and antisymmetric filters

Oversampled linear phase paraunitary filter bank (OLPPUFB) can be efficiently designed via lattice structure. Xu et al. have studied the lattice structure for arbitrary-length OLPPUFB (ALOLPPUFB), i.e. OLPPUFB with filter length KM + β, where M is the integer decimation factor, K is an integer, and β is an integer between 0 and M. Such work was restricted to be used for the case with equal numbers of symmetric and antisymmetric filters, and cannot be easily generalized for other possible cases. To address this issue, we develop in this letter the lattice structure for ALOLPPUFB with unequal numbers of symmetric and antisymmetric filters. The proposed method is carried out by combining the polyphase matrices of OLPPUFB with filter length KN, where N is the integer decimation factor, K is an integer. The efficiency of the method is shown by design examples.     

Linear phase paraunitary filter banks: theory, factorizations anddesigns

M channel maximally decimated filter banks have been used in the past to decompose signals into subbands. The theory of perfect-reconstruction filter banks has also been studied extensively. Nonparaunitary systems with linear phase filters have also been designed. The authors study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase. Specific instances of this problem have been addressed by other authors, and linear phase paraunitary systems have been shown to exist. This property is often desirable for several applications, particularly in image processing. They begin by answering several theoretical questions pertaining to linear phase paraunitary systems. Next, they develop a minimal factorization for a large class of such systems. This factorization will be proved to be complete for even M. Further, they structurally impose the additional condition that the filters satisfy pairwise mirror-image symmetry in the frequency domain. This significantly reduces the number of parameters to be optimized in the design process. They then demonstrate the use of these filter banks in the generation of M-band orthonormal wavelets. Several design examples are also given to validate the theory     

Technique for design of two-channel approximately linear phase QMFfilter bank and its application to image compression

The two-channel QMF filter bank based on allpass sections is one of the best known circuits for building up a multi-channel filter bank for signal compression. An analysis-synthesis combination can satisfy two of the three perfect reconstruction (PR) conditions. The third, the phase condition, can be met to any desired accuracy. However, when applied to images, PR is possible because non-causality can be allowed in the synthesis bank. The development of explicit formulae for the coefficients of such filters is considered. The resulting QMF designs can be used in a wavelet structure for image compression problems using rectangular or diamond symmetry. Several design examples are given, including a comparison of performance with FIR filter banks for such problems     

无抽样方向滤波器组的设计及其在医学图像增强中的应用

本文提出一种无抽样的方向滤波器组设计方法,并应用于医学图像增强.该方法将多级滤波器组整合为单级滤波器组,并将各频域滤波器均转化为w×w的空间模板,分别与图像卷积,获得各方向的子带图像,且每幅子带图像的分辨率均与原图像相同,便于利用各方向子带图像的统计特性,实现图像增强.实验结果表明:本方法因避免了抽样与插值过程,操作简便.采用图像方向特征,降低由于设备问题造成的图像模糊的影响,与其他常见的图像增强方法相比,其图像增强效果明显.     

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.     

Popular biorthogonal wavelet filters via a lifting scheme and its application in image compression

A technique using a lifting scheme is presented for constructing compactly supported wavelets whose coefficients are composed of free variables locating in an interval. An efficient approach-based wavelet for image compression is developed by selecting the coefficients of the 9-7 wavelet filter and associated lifting scheme. Furthermore, the rationalised coefficients wavelet filter that can be implemented with simple integer arithmetic is achieved and its characteristic is close to the well known original irrational coefficients 9-7 wavelet filters developed by A. Cohen et al. (Commun. Pure Appl. Maths., vol.45, no.1, p.485-560, 1992). To reduce the computational cost of image coding applications further, an acceleration technique is proposed for the lifting steps. Software and hardware simulations show that the new method has very low complexity, and simultaneously preserves the high quality of the compressed image.     

A new flexible bi-orthogonal filter design for multiresolutionfilterbanks with application to image compression

We propose a new fast method with great potential for multiresolution pyramid decomposition of signals and images. The method allows unusual flexibility in choosing a filter for any task involving the multiresolution analysis and synthesis. Using our method, one can choose any low-pass filter for the multiresolution filtering. This method enabled us to choose the best filters for set partitioning in hierarchical trees (SPIHT) image compression for the corresponding support sizes. The compression results for our seven tap filters are better than those of the 9/7 wavelet filters and approximately the same as those of the 10/18 filters, while at the same time our seven tap filters are faster than 10/18 filters     

A simplified lattice factorization for linear-phase paraunitary filter banks with pairwise mirror image frequency responses

In this paper, by extending our previous work on general linear-phase paraunitary filter banks even-channel (LPPUFBs), we develop a new structure for LPPUFBs with the pairwise mirror image (PMI) frequency responses, which is a simplified version of the lattice proposed by Nguyen et al. Our simplification is achieved through trivial matrix manipulations and the cosine-sine (C-S) decomposition of a general orthogonal matrix. The resulting new structure covers the same class of PMI-LPPUFBs as the original lattice, while substantially reducing the number of free parameters involved in the nonlinear optimization. A design example is presented to demonstrate the effectiveness of the new structure.     

New perspectives and improvements on the symmetric extension filter bank for subband/wavelet image compression.

In subband/wavelet image coding, size-limited subband decompositions are ordinarily used to avoid increasing the number of samples that need to be coded. To reduce coding distortions that can occur at the borders, the symmetric extension filter bank is typically employed. This paper introduces some new perspectives and improvements to that decomposition. The symmetric extension filter bank is couched in the cyclic frequency domain, providing a framework that accommodates FIR and IIR filters in a natural way, all with perfect reconstruction. IIR filters with both rational and irrational transfer functions can be implemented and, in the context of symmetric extension, can accommodate IIRs that effectively have perfect stopband suppression. Enhancements to the filter bank at a tree-structured system level are also presented and include the application of spectral reversal correction and a transition band normalization approach to designing the constituent filters of the symmetric extension wavelet packet transform.     

Linear-phase perfect reconstruction filter bank: lattice structure,design, and application in image coding

A lattice structure for an M-channel linear-phase perfect reconstruction filter bank (LPPRFB) based on the singular value decomposition (SVD) is introduced. The lattice can be proven to use a minimal number of delay elements and to completely span a large class of LPPRFBs: all analysis and synthesis filters have the same FIR length, sharing the same center of symmetry. The lattice also structurally enforces both linear-phase and perfect reconstruction properties, is capable of providing fast and efficient implementation, and avoids the costly matrix inversion problem in the optimization process. From a block transform perspective, the new lattice can be viewed as representing a family of generalized lapped biorthogonal transform (GLBT) with an arbitrary number of channels M and arbitrarily large overlap. The relaxation of the orthogonal constraint allows the GLBT to have significantly different analysis and synthesis basis functions, which can then be tailored appropriately to fit a particular application. Several design examples are presented along with a high-performance GLBT-based progressive image coder to demonstrate the potential of the new transforms     

Linear phase decimation and interpolation filters for high-speedapplications

A novel hardware realisation for linear phase decimation and interpolation FIR filters, exploiting the symmetry of the coefficients to reduce the number of multipliers, is described. Combining the multiplications, leads to contra-dataflow or folded filter structures in which simple pipelining is limited, because of the opposite directions of the data flows. It is shown that these structures can be transformed into new filter structures, which allow conventional pipelining to relax the timing demands for high-speed applications     

Novel phase lead inverting integrator and its application in two-integrator loop filters

A new variable phase inverting integrator is given. The proposed integrator is suitable for phase correction in the two integrator 1 filters.     

Technique for designing biorthogonal wavelet filters with anapplication to image compression

A technique for designing new symmetric biorthogonal wavelets from a given symmetric regular filter is presented. The main idea is to find a symmetric complementary filter of a given regular filter such that it has the least mean square (LMS) amplitude deviation from the ideal halfband lowpass filter. New biorthogonal wavelet filter pairs can be obtained via factoring the product of the complementary polynomial and the given binomial. By applying these new symmetric biorthogonal wavelet filters to the compression of some complicated images an improved result in reducing artefacts may be achieved     

CORDIC-lifting factorization of paraunitary filter banks based on the quaternionic multipliers for lossless image coding

Quaternions have offered a new paradigm to the signal processing community: to operate directly in a multidimensional domain. We have recently introduced the quaternionic approach to the design and implementation of paraunitary filter banks: four- and eight-channel linear-phase paraunitary filter banks, including those with pairwise-mirror-image symmetric frequency responses. The hypercomplex number theory is utilized to derive novel lattice structures in which quaternion multipliers replace Givens (planar) rotations. Unlike the conventional algorithms, the proposed computational schemes maintain losslessness regardless of their coefficient quantization. Moreover, the one regularity conditions can be expressed directly in terms of the quaternion lattice coefficients and thus easily satisfied even in finite-precision arithmetic. In this paper, a novel approach to realizing CORDIC-lifting factorization of paraunitary filter banks is presented, which is based on the embedding of the CORDIC algorithm inside the lifting scheme. Lifting allows for making multiplications invertible. The 2D CORDIC engine using sparse iterations and asynchronous pipeline processor architecture based on the embedded CORDIC engine as stage of processor is reported. Also it is necessary to notice, that the quaternion multiplier lifting scheme based on the 2D CORDIC algorithm is the structural decision for the lossless digital signal processing. This approach applies to very practical filter banks, which are essential for image processing, and addresses interesting theoretical questions.     

Theory and design of signal-adapted FIR paraunitary filter banks

We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks     

An entropy minimization histogram mergence scheme and its application in image compression

In this paper, we propose an entropy minimization histogram mergence (EMHM) scheme that can significantly reduce the number of grayscales with nonzero pixel populations (GSNPP) without visible loss to image quality. We proved in theory that the entropy of an image is reduced after histogram mergence and that the reduction in entropy is maximized using our EMHM. The reduction in image entropy is good for entropy encoding considering that the minimum average code word length per source symbol is the entropy of the source signal according to Shannon’s first theorem. Extensive experimental results show that our EMHM can significantly reduce the code length of entropy coding, such as Huffman, Shannon, and arithmetic coding, by over 20% while preserving the image subjective and objective quality very well. Moreover, the performance of some classic lossy image compression techniques, such as the Joint Photographic Experts Group (JPEG), JPEG2000, and Better Portable Graphics (BPG), can be improved by preprocessing images using our EMHM.     

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.     

余弦调制滤波器组的时频分析的等价性及其应用

该文通过证明 TDAC余弦调制滤波器组时域和频域分析的 PR条件的等价性,建立了 TDAC和 CMF分析技术的内在联系。并针对音频信号处理中往往根据人耳听觉的临界子带特性对信号进行非等带宽滤波,运用已有的一种 CMF非等带宽余弦调制滤波器组构造技术构造了一个 TDAC非等带宽余弦调制滤波器组。     

多级方向加权最小二乘滤波器及其在多传感器图像融合中的应用

针对多尺度分解在图像融合领域中的广泛应用,本文提出了一种多级方向加权最小二乘滤波器图像多尺度几何分析方法。该方法利用加权最小二乘滤波器对图像进行多级边缘保持分解,得到一个近似图像和多个不同尺度上的细节图像,然后采用小尺寸方向剪切滤波器对细节图像进行方向分析,在不同尺度上生成多个方向细节图像。根据近似图像和方向细节图像所具有的不同物理意义,分别采用不同的融合策略对分解后的图像系数进行合并处理,最后应用多级方向加权最小二乘滤波器的逆变换得到融合图像。多组图像融合实验结果表明,在图像融合领域,本文提出的基于多级方向加权最小二乘滤波器的图像分解方法优于已有文献中的一些典型多尺度分解方法。     

Novel fuzzy reinforced learning vector quantisation algorithm and its application in image compression

A new approach to the design of optimised codebooks using vector quantisation (VQ) is presented. A strategy of reinforced learning (RL) is proposed which exploits the advantages offered by fuzzy clustering algorithms, competitive learning and knowledge of training vector and codevector configurations. Results are compared with the performance of the generalised Lloyd algorithm (GLA) and the fuzzy K-means (FKM) algorithm. It has been found that the proposed algorithm, fuzzy reinforced learning vector quantisation (FRLVQ), yields an improved quality of codebook design in an image compression application when FRLVQ is used as a pre-process. The investigations have also indicated that RL is insensitive to the selection of both the initial codebook and a learning rate control parameter, which is the only additional parameter introduced by RL from the standard FKM