Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform

The energy compaction and multiresolution properties of wavelets have made the image fusion successful in combining important features such as edges and textures from source images without introducing any artifacts for context enhancement and situational awareness. The wavelet transform is visualized as a convolution of wavelet filter coefficients with the image under consideration and is computationally intensive. The advent of lifting-based wavelets has reduced the computations but at the cost of visual quality and performance of the fused image. To retain the visual quality and performance of the fused image with reduced computations, a discrete cosine harmonic wavelet (DCHWT)-based image fusion is proposed. The performance of DCHWT is compared with both convolution and lifting-based image fusion approaches. It is found that the performance of DCHWT is similar to convolution-based wavelets and superior/similar to lifting-based wavelets. Also, the computational complexity (in terms of additions and multiplications) of the proposed method scores over convolution-based wavelets and is competitive to lifting-based wavelets.     

Efficient implementation of lifting-based discrete wavelettransform

A recursive architecture for implementing the lifting-based discrete wavelet transform is proposed. Processing of the transform stages is interleaved, improving the hardware utilisation and efficiency, by exploiting the wavelet decimation structure     

Lifting-based wavelet domain adaptive Wiener filter for image enhancement

A method of applying lifting-based wavelet domain Wiener filter (LBWDMF) in image enhancement is proposed. Lifting schemes have emerged as a powerful method for implementing biorthogonal wavelet filters. They exploit the similarity of the filter coefficients between the low-pass and high-pass filters to provide a higher speed of execution, compared to classical wavelet transforms. LBWDMF not only helps in reducing the number of computations but also achieves lossy to lossless performance with finite precision. The proposed method utilises the multi-scale characteristics of the wavelet transform and the local statistics of each subband. The proposed method transforms an image into the wavelet domain using lifting-based wavelet filters and then applies a Wiener filter in the wavelet domain and finally transforms the result into the spatial domain. When the peak signal-to-noise ratio (PSNR) is low, transforming an image to the lifting-based wavelet domain and applying the Wiener filter in the wavelet domain produces better results than directly applying Wiener filter in spatial domain. In other words each subband is processed independently in the wavelet domain by a Wiener filter. Moreover, in order to validate the effectiveness of the proposed method the result obtained using the proposed method is compared to those using the spatial domain Wiener filter (SDWF) and classical wavelet domain Wiener filter (CWDWF). Experimental results show that the proposed method has better performance over SDWF and CWDWF both visually and in terms of PSNR.     

A comparison of hardware implementations of the biorthogonal 9/7 DWT: convolution versus lifting

The filter bank approach for computing the discrete wavelet transform (DWT), which we call the convolution method, can employ either a nonpolyphase or polyphase structure. This work compares filter banks with an alternative polyphase structure for calculating the DWT-the lifting method. We look at the traditional lifting structure and a recently proposed "flipping" structure for implementing lifting. All filter bank structures are implemented on an Altera field-programmable gate array. The quantization of the coefficients (for implementation in fixed-point hardware) plays a crucial role in the performance of all structures, affecting both image compression quality and hardware metrics. We design several quantization methods and compare the best design for each approach: the nonpolyphase filter bank, the polyphase filter bank, the lifting and flipping structures. The results indicate that for the same image compression performance, the flipping structure gives the smallest and fastest, low-power hardware.     

Fast spatial combinative lifting algorithm of wavelet transformusing the 9/7 filter for image block compression

A new fast spatial combinative lifting algorithm (SCLA) of the wavelet transform using the 9/7 filter for image block compression is proposed. In comparison with its lifting-based implementation, the number of multiplications is reduced by a ratio of 5/12 and the speed of implementation of the wavelet transform is increased     

二维离散5/3小波变换并行VLSI结构设计

提出了一种基于提升算法的二维离散5/3小波变换(DWT)高效并行VLSI结构设计方法。该方法使得行和列滤波器同时进行滤波,采用流水线设计方法处理,在保证同样的精度下,大大减少了运算量,提高了变换速度,节约了硬件资源。该方法已通过了VerilogHDL行为级仿真验证,可作为单独的IP核应用在JPEG2000图像编、解码芯片中。该结构可推广到9/7小波提升结构。     

Efficient VLSI Architecture for Lifting-Based Discrete Wavelet Packet Transform

This brief presents a novel very large-scale integration (VLSI) architecture for discrete wavelet packet transform (DWPT). By exploiting the in-place nature of the DWPT algorithm, this architecture has an efficient pipeline structure to implement high-throughput processing without any on-chip memory/first-in first out access. A folded architecture for lifting-based wavelet filters is proposed to compute the wavelet butterflies in different groups simultaneously at each decomposition level. According to the comparison results, the proposed VLSI architecture is more efficient than the previous proposed architectures in terms of memory access, hardware regularity and simplicity, and throughput. The folded architecture not only achieves a significant reduction in hardware cost but also maintains both the hardware utilization and high-throughput processing with comparison to the direct mapped tree-structured architecture     

Perceptual Audio Coding Using Sinusoidal/Optimum Wavelet Representation

A perceptual audio coder, in which each audio segment is adaptively analyzed using either a sinusoidal or an optimum wavelet basis according to the time-varying characteristics of the audio signals, has been constructed. The basis optimization is achieved by a novel switched filter bank scheme, which switches between a uniform filter bank structure (discrete cosine transform) and a non-uniform filter bank structure (discrete wavelet transform). A major artifact of the International ISO/Moving Pictures Experts Group (MPEG) audio coding standard (MPEG-I layers 1 and 2) known as pre-echo distortion which uses a uniform filter bank structure for audio signal analysis, is almost eliminated in the proposed coder. A perceptual masking model implemented using a high-resolution wavelet packet filter bank with 27 subbands, closely mimicking the critical bands of the human auditory system, is employed in this audio coder. The resulting scheme is a variable bit-rate audio coder, which provides compression ratios comparable to MPEG-I layers 1 and 2 with almost transparent quality.     

一维离散小波变换VLSI结构分析设计

提升算法的推出使得离散小波变换硬件的快速实现成为可能。翻转结构在提升架构的基础上进一步提高运算速度。在此,对翻转结构的舍入误差进行了分析,在翻转结构的基础上,对提升步骤进行了合并,提出一种有效的DWT硬件实现方案。实验结果表明,通过采用流水线模式提出的这种硬件结构,在关键路径约束的条件下,可以充分利用硬件资源。     

Weighted Adaptive Lifting-Based Wavelet Transform for Image Coding

In this paper, a new weighted adaptive lifting (WAL)-based wavelet transform is presented. The proposed WAL approach is designed to solve the problems existing in the previous adaptive directional lifting (ADL) approach, such as mismatch between the predict and update steps, interpolation favoring only horizontal or vertical direction, and invariant interpolation filter coefficients for all images. The main contribution of the proposed approach consists of two parts: one is the improved weighted lifting, which maintains the consistency between the predict and update steps as far as possible and preserves the perfect reconstruction at the same time; another is the directional adaptive interpolation, which improves the orientation property of the interpolated image and adapts to statistical property of each image. Experimental results show that the proposed WAL-based wavelet transform for image coding outperforms the conventional lifting-based wavelet transform up to 3.06 dB in PSNR and significant improvement in subjective quality is also observed. Compared with the ADL-based wavelet transform, up to 1.22-dB improvement in PSNR is reported.     

Edge-preserving image compression using adaptive lifting wavelet transform

In this paper, a novel 2-D adaptive lifting wavelet transform is presented. The proposed algorithm is designed to further reduce the high-frequency energy of wavelet transform, improve the image compression efficiency and preserve the edge or texture of original images more effectively. In this paper, a new optional direction set, covering the surrounding integer pixels and sub-pixels, is designed. Hence, our algorithm adapts far better to the image orientation features in local image blocks. To obtain the computationally efficient and coding performance, the complete processes of 2-D adaptive lifting wavelet transform is introduced and implemented. Compared with the traditional lifting-based wavelet transform, the adaptive directional lifting and the direction-adaptive discrete wavelet transform, the new structure reduces the high-frequency wavelet coefficients more effectively, and the texture structures of the reconstructed images are more refined and clear than that of the other methods. The peak signal-to-noise ratio and the subjective quality of the reconstructed images are significantly improved.     

Self-lifting scheme: new approach for generating and factoring wavelet filter bank

The authors presents a new lifting scheme, the self-lifting scheme, and prove that self-lifted wavelets based on orthogonal or biorthogonal wavelets remain biorthogonal. In contrast to self-lifting, the existing lifting scheme can be called cross-lifting. Compared with cross-lifting, the self-lifting scheme provides new approaches for constructing biorthogonal wavelets, as well as factorising wavelet filter bank (WFB). For constructing wavelets, the self-lifting-based method updates one part of a wavelet filter by the other part of the same filter and obtains two updated filters in one pass, whereas the cross-lifting based method updates one filter by another filter and obtains one updated filter in one pass. To factorise WFB, self-lifting takes one part of a filter as the factor to decompose the other part of the same filter and obtains two factorised filters in one pass, whereas crosslifting based one takes one part of a filter as the factor to decompose the corresponding part of the other filter and obtains one factorised filter in one pass. Several examples show how to use self-lifting scheme to produce new wavelets with desirable properties, how to factorise complex WFBs into simple lifting filter banks, how to implement self-lifting-based discrete wavelet transform (WT) in z-domain and in time domain and why lifting-based WT is superior to convolution-based one.     

Computation of DWT via FHT-based implementation

It is well known that most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform (DWT). Although this method is efficient, noticeable computational savings have been obtained through an FFT-based implementation. The authors present a fast Hartley transform (FHT)-based implementation of the filter bank and show that noticeable overall computational savings can be obtained     

Subband Weighting With Pixel Connectivity for 3-D Wavelet Coding

Performing optimal bit-allocation with 3-D wavelet coding methods is difficult because energy is not conserved after applying the motion-compensated temporal filtering (MCTF) process and the spatial wavelet transform. The problem cannot be solved by extending the 2-D wavelet coefficients weighting method directly and then applying the result to 3-D wavelet coefficients, since this approach does not consider the complicated pixel connectivity that results from the lifting-based MCTF process. In this paper, we propose a novel weighting method, which takes account of the pixel connectivity, to solve the problem and derive the effect of the quantization error of a subband on the reconstruction error of a group of pictures. We employ the proposed method on a ${hbox {2-D}}+{rm t}$ structure with different temporal filters, namely the 5-3 filter and the 9-7 filter. Experiments on various coding parameters and sequences show that the proposed approach improves the bit-allocation performance over that obtained by using the weightings derived without considering the pixel connectivity in the MCTF process.      

Lossless image compression with projection-based and adaptive reversible integer wavelet transforms

Reversible integer wavelet transforms are increasingly popular in lossless image compression, as evidenced by their use in the recently developed JPEG2000 image coding standard. In this paper, a projection-based technique is presented for decreasing the first-order entropy of transform coefficients and improving the lossless compression performance of reversible integer wavelet transforms. The projection technique is developed and used to predict a wavelet transform coefficient as a linear combination of other wavelet transform coefficients. It yields optimal fixed prediction steps for lifting-based wavelet transforms and unifies many wavelet-based lossless image compression results found in the literature. Additionally, the projection technique is used in an adaptive prediction scheme that varies the final prediction step of the lifting-based transform based on a modeling context. Compared to current fixed and adaptive lifting-based transforms, the projection technique produces improved reversible integer wavelet transforms with superior lossless compression performance. It also provides a generalized framework that explains and unifies many previous results in wavelet-based lossless image compression.     

Speech frame recognition based on less shift sensitive wavelet filter banks

The wavelet transform possesses multi-resolution property and high localization performance; hence, it can be optimized for speech recognition. In our previous work, we show that redundant wavelet filter bank parameters work better in speech recognition task, because they are much less shift sensitive than those of critically sampled discrete wavelet transform (DWT). In this paper, three types of wavelet representations are introduced, including features based on dual-tree complex wavelet transform (DT-CWT), perceptual dual-tree complex wavelet transform, and four-channel double-density discrete wavelet transform (FCDDDWT). Then, appropriate filter values for DT-CWT and FCDDDWT are proposed. The performances of the proposed wavelet representations are compared in a phoneme recognition task using special form of the time-delay neural networks. Performance evaluations confirm that dual-tree complex wavelet filter banks outperform conventional DWT in speech recognition systems. The proposed perceptual dual-tree complex wavelet filter bank results in up to approximately 9.82 % recognition rate increase, compared to the critically sampled two-channel wavelet filter bank.     

Design of prefilters for discrete multiwavelet transforms

The pyramid algorithm for computing single wavelet transform coefficients is well known. The pyramid algorithm can be implemented by using tree-structured multirate filter banks. The authors propose a general algorithm to compute multiwavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets. The proposed algorithm can be thought of as a discrete vector-valued wavelet transform for certain discrete-time vector-valued signals. The proposed algorithm can be also thought of as a discrete multiwavelet transform for discrete-time signals. The authors then present some numerical experiments to illustrate the performance of the algorithm, which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms     

Implementation of RNS-Based Distributed Arithmetic Discrete Wavelet Transform Architectures Using Field-Programmable Logic

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength).     

The discrete wavelet transform: wedding the a trous and Mallatalgorithms

Two separately motivated implementations of the wavelet transform are brought together. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by the choice of filters. In fact, the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Relevant signal processing parameters are examined, and it is observed that orthonormality is balanced by restrictions on resolution     

Low power embedded extension algorithm for lifting-based discretewavelet transform in JPEG2000

A novel algorithmic technique for reducing power and area consumption of the discrete wavelet transform (DWT) on CMOS-based DSP architectures is presented. The technique reduces power by combining the data-extension procedure into the lifting-based DWT core. It is demonstrated that the new algorithm can be used to obtain more than 50% reduction in the amount of memory required, leading to significant reduction in area and power