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     

多维DFT的多维多项式变换与离散W变换算法

本文首先通过引进一种序列的重排技术将m(m2) 维离散Fourier变换 (m-D DFT)转化为一系列的一维广义离散Fourier变换(GDFT)的多重和.然后引入一维离散W变换(DWT)以及多维多项式变换(MD-PT)计算该多重和以减少冗余的算术运算,从而得到了高效的多维DFT算法,该算法与常用的行-列DFT算法相比,乘法仅约为行-列法的1/2m,而加法仅约为行-列法的(2m+1)/4m.对于2维DFT的计算,本文方法同单纯的多项式变换方法相比,乘法与加法分别减少50%与40%左右.另外,本文算法计算结构简单,易于编程实现,通过数值实验验证了本文算法的高效性.     

A prime factor FFT algorithm with real valued arithmetic

A prime factor FFT algorithm involving only real valued arithmetic is devised to compute the discrete Fourier transform of a real sequence. This letter extends an approach proposed by Bracewell.     

Inverse Z-transform by Mobius inversion and the error bounds ofaliasing in sampling

A general algorithm based on two special Mobius inversion formulae is developed to compute the inverse Z-transform. This approach to Fourier analysis uses what is called the arithmetic Fourier transform (AFT). With the new AFT algorithm. One can compute the inverse Z-transform of an infinite two-sided sequence. It is compared with the conventional DFT approach. Both methods have aliasing errors due to sampling. The error bounds of the aliasing effects in the DFT and the new proposed method are established and compared. In general, the AFT algorithm is not so vulnerable to the aliasing errors in the high-frequency components as the DFT approach     

An efficient algorithm for sensitivity analysis of nonuniform transmission lines

This paper presents a new algorithm that addresses an important issue arising in computation of sensitivity for nonuniform transmission lines using the idea of model reduction through integrated congruence transform. This issue is related extending the concept of implicit basis construction, which was introduced earlier to simulate nonuniform transmission lines, to the task of sensitivity analysis. A new algorithm is presented to compute the orthogonal basis needed to obtain the reduced system used in sensitivity analysis. The proposed algorithm incorporates a new orthogonalization procedure which can be used to find an orthogonal basis for a set of moments derived from inhomogeneous differential equations, but without having to compute those moments explicitly. Numerical results demonstrate that reduced-order systems constructed by the proposed algorithm have improved numerical accuracy in sensitivity computation.     

基于离散傅里叶变换和块时间递归并行格型结构的离散Gabor分析窗求解

提出了一种快速求解离散Gabor变换分析窗的方法.首先选择一个合适的基函数,同给定的综合窗函数构造一个可逆的块循环矩阵,然后根据块循环矩阵特点,利用快速离散傅里叶变换求解块循环矩阵的逆,最后采用基于块时间递归的并行格型结构来求解分析窗.本文证明了此算法获得的窗函数与给定的综合窗满足双正交关系.实验结果表明,本文算法能快...     

FPGA implementation of high-performance,resource-efficient Radix-16 CORDIC rotator based FFT algorithm

The fast Fourier transform (FFT) is an algorithm widely used to compute the discrete Fourier transform (DFT) in real-time digital signal processing. High-performance with fewer resources is highly desirable for any real-time application. Our proposed work presents the implementation of the radix-2 decimation-in-frequency (R2DIF) FFT algorithm based on the modified feed-forward double-path delay commutator (DDC) architecture on FPGA device. Need for a complex multiplier to carry out the multiplication of complex twiddle factors and large memory to store the twiddle factors are the main concerns for FFT implementation. Propose work aims to address these issues. In this work, a high-performance radix-16 COordinate Rotational DIgital Computer (CORDIC) algorithm based rotator is proposed to carry out the complex twiddle factor multiplication. Further, CORDIC needs only rotational angles to carry out complex multiplication, which reduces the need for large memory to store the twiddle factors. To compute the total rotation for n-bit precision, our proposed radix-16 CORDIC algorithm takes n/4 iteration as compared to n iteration of the radix-2 CORDIC algorithm. Our proposed architecture of the radix-2 decimation-in-frequency (R2DIF) algorithm is implemented on a Virtex−7 series FPGA. Further, the detailed comparison is presented between our proposed FFT implementation and other recently proposed FFT implementations. Experimental results suggest that proposed implementation has less latency and hardware utilization as compared to recently proposed implementations.     

Fast computation of discrete Hartley transform via Walsh?Hadamard transform

A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh?Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.     

Multidimensional Polynomial Transform Algorithm For Multidimensional Discrete Hartley Transform

In this paper, we present an index permutation-based fast algorithm for the multidimensional discrete Hartley transform (MD-DHT). By reordering the MD-DHT input sequence, we first convert the MD-DHT into a multiple sum that contains a number of one-dimensional discrete W transforms (1D-DWTs). We then use a combination of the 1D-DWTs and the multidimensional polynomial transform to compute the multiple sum. It is shown that the number of multiplications and additions required for the proposed algorithm are approximately 1/m and 2m+1/3m times that of the commonly used row-column DHT method, respectively. The developed algorithm is also simple in structure and easy to realize in programming.     

融合显性和隐性度量的多模图像配准算法

为解决基于隐性度量的图像配准算法初始配准误差大容易引起失配的问题,本文提出了一种融合显性度量和隐性度量的多模图像分层配准算法。首先采用金字塔分解算法得到低分辨率待配准图像。然后在每一层金字塔图像中,先采用互信息作为显性度量,利用粒子群算法获得初始的配准参数;以此作为初始值,采用基于隐性度量的配准算法,利用融合粒子群和鲍威尔搜索法的优化算法获取更准确的配准参数。基于低分辨率图像计算得到配准参数后,先对高分辨率待配准图像进行变换,然后利用提出的上述算法进行参数优化,根据每层得到的配准参数计算最终的配准参数。最后,采用可见光与红外图像、多波段SAR图像进行了配准实验。实验结果表明,提出的算法适用于多模图像配准,能够减小配准误差,具有一定的适用性。      

基于LMS算法的多点滑动DFT方法

 根据自适应LMS法,LMS谱分析器可以通过递归运算完成滑动窗口中数据的DFT运算.本文推导了LMS算法及多点滑动DFT运算之间的关系式,并由此提出了一种基于LMS算法的多点滑动DFT运算方法.文章在理论推导的同时,进行了计算机仿真验证.该方法使用方便,可灵活适用于不同的滑动窗口大小及滑动步长参数.     

An Efficient Algorithm for the Computation of the Multidimensional Discrete Fourier Transform

In this paper, we propose a new approach for computing multidimensional Cooley-Tukey FFT's that is suitable for implementation on a variety of multiprocessor architectures. Our algorithm is derived in this paper from a Cooley decimation-in-time algorithm by using an appropriate indexing process and the tensor product properties. It is proved that the number of multiplications necessary to compute our proposed algorithm is significantly reduced while the number of additions remains almost identical to that of conventional Multidimensional FFT's (MFFT). Comparison results show the powerful performance of the proposed MFFT algorithm against the row-column FFT transform when data dimension M is large. Furthermore, this algorithm, presented in a simple matrix form, will be much easier to implement in practice. Connections of the proposed approach with well-known DFT algorithms are included in this paper and many variations of the proposed algorithm are also pointed out.     

Recursive pruning of the 2D DFT with 3D signal processingapplications

A recursively pruned radix-(2×2) two-dimensional (2D) fast Fourier transform (FFT) algorithm is proposed to reduce the number of operations involved in the calculation of the 2D discrete Fourier transform (DFT). It is able to compute input and output data points having multiple and possibly irregularly shaped (nonsquare) regions of support. The computational performance of the recursively pruned radix-(2×2) 2D FFT algorithm is compared with that of pruning algorithms based on the one-dimensional (1D) FFT. The former is shown to yield significant computational savings when employed in the combined 2D DFT/1D linear difference equation filter method to enhance three-dimensional spatially planar image sequences, and when employed in the MixeD moving object detection and trajectory estimation algorithm     

Efficient simulation of nonuniform transmission lines using integrated congruence transform

This paper presents a new algorithm based on integrated congruence transform for efficient simulation of nonuniform transmission lines. The proposed algorithm introduces the concept of model-order reduction (MOR) via implicit usage of the Hilbert-space moments in distributed networks. The key idea in the proposed algorithm is the development of an orthogonalization procedure that does not require the explicit computation of the Hilbert-space moments in order to find their spanning orthogonal basis. The proposed orthogonalization procedure can thus be used to compute an orthogonal basis for any set of elements that are related through a differential operator in a generalized Hilbert space, without the need to have these elements in an explicit form. The proposed algorithm also addresses the problem of MOR of nonuniform transmission lines, through defining a weighted inner product and norm mappings over the Hilbert space of the moments. Numerical examples demonstrate more accurate numerical approximation capabilities over using the moments explicitly.     

Accelerating the nonequispaced fast Fourier transform on commodity graphics hardware

We present a fast parallel algorithm to compute the nonequispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform as it was previously its most time consuming part. We describe the performance for two common sample distributions in medical imaging (radial and spiral trajectories), and for different convolution kernels as these parameters all influence the speed of the algorithm. The GPU-accelerated convolution is up to 85 times faster as our reference, the open source NFFT library on a state-of-the-art 64 bit CPU. The accuracy of the proposed GPU implementation was quantitatively evaluated at the various settings. To illustrate the applicability of the transform in medical imaging, in which it is also known as gridding, we look specifically at non-Cartesian magnetic resonance imaging and reconstruct both a numerical phantom and an in vivo cardiac image.     

一种基于小波的多光谱图像压缩方法

文章提出一种基于Karhunen2Loeve变换(KLT)和小波量化编码的多光谱图像压缩方法。该法首先使用KL变换步骤来去除谱间冗余,而后对各变换波段图像进行小波变换,并利用均匀阈值网格编码量化方法来量化小波子带图像,最后使用算术编码对量化结果进行熵编码。为使编码器能为所有谱段各子带获取率- 失真意义上最优的量化阈值,本文提出基于子带图像统计特性和网格编码量化器率- 失真特性的比特分配算法。实验表明,本方法能高效地压缩多光谱图像,表现出优异的压缩性能。     

一种新的三维离散Hartley变换的分裂基快速算法

 离散Hartley变换(Discrete Hartley Transform,DHT)作为实值离散傅立叶变换的一种替代,在信号和图像处理领域已有广泛应用,针对现有三维DHT快速算法均仅能计算长度为2的整数次幂的DHT,本文提出一种适用于更多不同长度三维DHT的分裂基-2/4快速算法,较之将已有最优算法补零计算的方法,该算法有效的降低了计算复杂度.     

改进的Hough变换及其并行计算

本文针对传统的Ｈｏｕｇｈ变换不能测出直线的连贯性、无法求得线段的长度的缺点，提出一种改进的Ｈｏｕｇｈ变换算法，使检测结果为线段的起始及长度。     

基于分形维数和FCM聚类的多时相SAR图像变化检测

提出了一种基于分形维数和FCM聚类的SAR图像无监督变化检测的算法。首先用非下采样Contourlet变换(NSCT),对两时相图像进行分解,然后求出其分形维数图,构造差异图,再由FCM聚类得到变化区域和非变化区域。并对计算分形维的滑动窗口大小的选择进行了研究。与现有的基于分形维数的图像变化检测算法进行对比,实验证实,本文算法不仅对斑点噪声不敏感,并且提高了变化检测的精确度。     

基于QR分解的最大负熵盲分离算法

提出了一种新的实时线性混叠信号盲分离算法。该算法先采取白化混叠信号将混叠矩阵转换为正交矩阵,然后基于QR分解理论,并结合源信号相互独立时负熵最大的特点而导出。该方法避免了目前许多学习算法中矩阵逆的计算,从而大大地减少了分离的计算量。理论分析与仿真结果表明该算法不仅具有很好的分离效果,而且也减少了分离时间,其效果均优于Andrzej(1996)和Pham(1999)的相应结果。