基于DCT的实值离散Gabor变换

该文提出了一种基于离散余弦变换(DCT)的实值离散Gabor变换(RDGT),不仅适用于临界抽样条件而且适用于过抽样条件,并证明了变换的完备性条件。由于这种变换仅涉及实值计算,并且可利用快速DCT,IDCT算法来加速运算,因此比传统复值离散Gabor变换在计算和实现方面更为简单,必将有效地提高非平稳信号与图像的分析、处理速度和效率。     

二维实值离散Gabor变换时间递归算法的双层并行格型结构实现方法

本文首先简单回顾了作者曾提出的二维实值离散Gabor变换及其与复值离散Gabor变换的简单关系，然后着重探讨了二维实值离散Gabor变换快速计算问题，提出了二维实值离散Gabor变换系数求解的时间递归算法以及由变换系数重构原图像的块时间递归算法，研究了双层并行格型结构实现算法的方法，计算复杂性分析及与其它算法的比较证明了双层并行格型结构实现方法在实时处理方面的优越性。     

Multirate-based fast parallel algorithms for DCT-kernel-based real-valued discrete Gabor transform

Fast parallel algorithms for the DCT-kernel-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented based on multirate signal processing. An analysis convolver bank is designed for the RDGT and a synthesis convolver bank is designed for its inverse transform. The parallel channels in each of the two convolver banks have a unified structure and can apply the fast DCT algorithms to reduce computation. The computational complexity of each parallel channel is low and depends mainly on the length of the discrete input signal and the number of the Gabor frequency sampling points. Every parallel channel corresponds to one RDGT coefficient, and all the RDGT coefficients are computed in parallel during the analysis process and are finally reconstructed in parallel as pieces of the original signal during the synthesis process. The computational complexity related to the computational time of each RDGT coefficient or each piece of the reconstructed signal in the proposed parallel algorithms is analyzed and compared with those in the existing major parallel algorithms for the RDGT and its inverse transform. The results indicate that the proposed multirate-based fast parallel algorithms for the RDGT are attractive for real-time signal processing.     

实值离散Gabor变换块时间递归算法的并行格型结构实现方法

Gabor变换在很多领域被认为是非常有用的方法,如语音与图像处理,雷达、声纳、振动信号的处理与理解等,然而实时应用却因其很高的计算复杂性而受到限制.为了减小计算复杂性,我们曾提出了实值离散Gabor变换法.本文首先简单回顾了作者曾提出的实值离散Gabor变换及其与复值离散Gabor变换的关系,然后为了有效地和快速地计算实值离散Gabor变换,提出了在临界抽样条件下和在过抽样条件下,一维实值离散Gabor变换系数求解的块时间递归算法以及由变换系数重建原信号的块时间递归算法,研究了两算法使用并行格型结构的实现方法,并讨论和比较了算法的计算复杂性和优越性.     

Multirate-based fast parallel algorithms for 2-D DHT-based real-valued discrete Gabor transform

Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.     

Fast Parallel Approach for 2-D DHT-Based Real-Valued Discrete Gabor Transform

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.      

Oversampled Gabor representation for transient signals

Considers the Gabor representation that uses a one-sided exponential window for detection and analysis of transient signals. Earlier results on the critically sampled case are extended to the more practically useful oversampled case. For oversampling by an integer factor, the authors derive an explicit analytical expression for the dual window (dual frame) function required for computing the Gabor representation. Based on this expression they develop an efficient procedure for computing the Gabor coefficients. Finally, they demonstrate the performance of the method by numerical examples     

Efficient Parallel Computing-Based Implementation Methods of DCT-Kernel-Based Real-Valued Discrete Gabor Transform and Expansion

Journal of Signal Processing Systems - The existing researches of fast parallel algorithms for DCT-based real-valued discrete Gabor transform and expansion are limited to theoretical analysis. In...     

The generalized Gabor transform

The generalized Gabor transform (for image representation) is discussed. For a given function f(t), tinR, the generalized Gabor transform finds a set of coefficients a(mr) such that f(t)=Sigma(m=-infinity)(infinity)Sigma (r=-infinity)(infinity)alpha(mr )g(t-mT)exp(i2pirt/T'). The original Gabor transform proposed by D. Gabor (1946) is the special case of T=T'. The computation of the generalized Gabor transform with biorthogonal functions is discussed. The optimal biorthogonal functions are discussed. A relation between a window function and its optimal biorthogonal function is presented based on the Zak (1967) transform when T/T' is rational. The finite discrete generalized Gabor transform is also derived. Methods of computation for the biorthogonal function are discussed. The relation between a window function and its optimal biorthogonal function derived for the continuous variable generalized Gabor transform can be extended to the finite discrete case. Efficient algorithms for the optimal biorthogonal function and generalized Gabor transform for the finite discrete case are proposed.     

The quantized DCT and its application to DCT-based video coding

The two-dimensional (2-D) discrete cosine transform (DCT) and the subsequent quantization of the transform coefficients are two computationally demanding steps of any DCT-based video encoder. In this paper, we propose an efficient joint implementation of these two steps, where the precision in computing the DCT can be exchanged for a reduction in the computational complexity. First, the quantization is embedded in the DCT, thus eliminating the need to explicitly quantize the transform coefficients. A multiplierless integer implementation of the quantized DCT (QDCT) is then proposed that performs shift and add operations instead of full multiplications. A sequence of multiplierless QDCT algorithms is obtained with increasing precision and number of computations. Finally, further savings in computations are obtained by terminating the DCT computations whenever intermediate results indicate that the transform and quantization steps will likely result in a block of zero values. The proposed algorithms are applied to, and results are presented for, high-quality MPEG-2 and low bit rate H.263 video encoding.     

Order N log2 N WHT/DHT algorithm

An efficient algorithm is proposed which computes the coefficients of the higher order discrete Hartley transform (DHT) directly from the coefficients of lower-order DHTs. With this new development, the two-stage Walsh-Hadamard transform/discrete Hartley transform (WHT/DHT) is comparable to the existing fast algorithms. The same approach can also be used for the computation of DCT coefficients     

Design of M‐Channel IIR Uniform DFT Filter Banks Using Recursive Digital Filters

In this paper, we propose a method for designing a class of M‐channel, causal, stable, perfect reconstruction, infinite impulse response (IIR), and parallel uniform discrete Fourier transform (DFT) filter banks. It is based on a previously proposed structure by Martinez et al. [1] for IIR digital filter design for sampling rate reduction. The proposed filter bank has a modular structure and is therefore very well suited for VLSI implementation. Moreover, the current structure is more efficient in terms of computational complexity than the most general IIR DFT filter bank, and this results in a reduced computational complexity by more than 50% in both the critically sampled and oversampled cases. In the polyphase oversampled DFT filter bank case, we get flexible stop‐band attenuation, which is also taken care of in the proposed algorithm.     

Fast DCT domain filtering using the DCT and the DST

A method for efficient spatial domain filtering, directly in the discrete cosine transform (DCT) domain, is developed and proposed. It consists of using the discrete sine transform (DST) and the DCT for transform-domain processing on the in JPEG basis of the previously derived convolution-multiplication properties of discrete trigonometric transforms. The proposed scheme requires neither zero padding of the input data nor kernel symmetry. It is demonstrated that, in typical applications, the proposed algorithm is significantly more efficient than the conventional filtered spatial domain and earlier proposed DCT domain methods. The proposed method is applicable to any DCT-based image compression standard, such as JPEG, MPEG, and H.261.     

二维滑动矩形窗傅氏变换的快速递推算法

该文利用相邻滑动窗数据之间的关系以及傅氏变换的平移性质,提出一种二维滑动矩形窗傅氏变换的快速递推算法。文中分析了该快速递推算法的复杂度和传统直接计算法的复杂度,证明了新的快速递推法可以大大降低计算复杂性,尤其是在图像尺寸和窗口尺寸较大的场合中。该算法可以改善滑窗傅氏变换或Gabor变换的计算效率。     

实值离散GABOR变换的最优双正交分析窗函数

Ｇａｂｏｒ变换在信号图像处理中是一非常有用的工具。本文首先回顾了作者曾提出的实值离散Ｇａｂｏｒ变换方法,然后着重讨论了在已知综合窗函数条件下,双正交分析窗函数的最优解问题,指出在许多情况下,这些最优解（如最小范数解与最似正交解）都是相同的,并讨论了采用奇异值分解（ＳＶＤ）理论求解双正交分析窗函数的方法。文末还给出了求解了实例。     

An efficient algorithm to compute the complete set of discreteGabor coefficients

The discrete Gabor (1946) transform algorithm is introduced that provides an efficient method of calculating the complete set of discrete Gabor coefficients of a finite-duration discrete signal from finite summations and to reconstruct the original signal exactly from the computed expansion coefficients. The similarity of the formulas between the discrete Gabor transform and the discrete Fourier transform enables one to employ the FFT algorithms in the computation. The discrete 1-D Gabor transform algorithm can be extended to 2-D as well.     

Discrete multi-Gabor expansions

A discrete multi-Gabor expansion (DMGE) is developed to meet the requirements of localized and refined time-frequency (TF) representation of signals. The DMGE uses multiple windows and their translations and complex modulations as synthesis (or analysis) waveforms. It includes and generalizes the metaplectic (translation, modulation, and dilation) representations which are useful in signal analysis. Uniform, nonuniform, and proportional time sampling schemes are analyzed. The fundamental features and the importance of the DMGE are discussed. We focus on the construction of DMGE and deriving fast algorithms for the computation of related multi-analysis sequences. With matrix algebra, the algorithms derived apply to both multi-Gabor expansions and uni-(window) Gabor expansions. Another useful feature of the DMGE lies in the fact that the multi-Gabor transform can be realized in a parallel FFT-based implementation structure. Examples of DMGE and their applications to TF analysis are also discussed     

DCT快速算法及其VLSI实现

现在离散余弦变换（DCT）发展很快，本文概述了DCT的各种快速算法及其发展，将DCT算法进行了分类。文中详细地综述了适合于VLSI实现的各种DCT算法结构，并对这一领域的发展及应用前景进行了探讨。     

On the Error-Free Realization of a Scaled DCT Algorithm and Its VLSI Implementation

This brief is concerned with the efficient and error-free implementation of the order-8 Linzer-Feig (L-F) scaled discrete cosine transform (sDCT). We present a novel 3-D algebraic integer encoding scheme which maps the transform basis functions (transcendental functions such as cosine and tangent) with integer values, so that the quantization errors can be minimized and the cross-multiplications (in the signal path) can be avoided. This scheme also allows the separable computation of a 2-D DCT in multiplication-free, fast, and efficient architectures with a process rate of 80 mega-samples/sec. The proposed scheme also reduces the latency and the power consumption compared to previously employed designs for DCT implementations.