Efficient implementation of discrete Pascal transform using difference operators

An alternative way is provided to define the discrete Pascal transform using difference operators to reveal the fundamental concept of the transform, in both one- and two-dimensional cases, which is extended to cover non-square two-dimensional applications. Efficient modularised implementations are proposed.     

Optimal transform coding in the presence of quantization noise

The optimal linear Karhunen-Loeve transform (KLT) attains the minimum reconstruction error for a fixed number of transform coefficients assuming that these coefficients do not contain noise. In any real coding system, however, the representation of the coefficients using a finite number of bits requires the presence of quantizers. We formulate the optimal linear transform using a data model that incorporates the quantization noise. Our solution does not correspond to an orthogonal transform and in fact, it achieves a smaller mean squared error (MSE) compared to the KLT, in the noisy case. Like the KLT, our solution depends on the statistics of the input signal, but it also depends on the bit-rate used for each coefficient. Especially for images, based on our optimality theory, we propose a simple modification of the discrete cosine transform (DCT). Our coding experiments show a peak signal-to noise ratio (SNR) performance improvement over JPEG of the order of 0.2 dB with an overhead less than 0.01 b/pixel.     

窗口傅里叶变换的三维面形测量

由于窗口傅里叶变换具布局部分析特性,且局部谱比全局的谱更简单、更不容易频谱混叠。本文提出在基于频谱分析的三维面形测量中,用窗口傅里叶变换（WFT）代替传统的快速傅里叶变换（FFT）去获取三维物体面形分布。理论分析和实验结果表明：窗口傅里叶变换不但可以减小频谱混叠对测量精度的影响,并且若在窗口傅里叶变换的处理过程中,设置合理的“门限”,还能够有效的抑制噪声。从而在一定程度上保证了基于频谱分析的三维面形测量的精度。     

Computation of 2D discrete Hartley transform

Based on a decimation-in-time decomposition, a fast split-radix algorithm for the 2D discrete Hartley transform is presented. Compared to other reported algorithms, the proposed algorithm achieves substantial savings on the number of operations and provides a wider choice of transform sizes     

Computation of the discrete cosine transform using the iterative arithmetic fourier transform

A method of computing the discrete cosine transform using the iterative arithmetic Fourier transform is presented. It overcomes the difficulty of dense, Farey-fraction sampling in the time domain or space domain when using the original arithmetic Fourier transform (AFT) algorithm. Also, dense transform-domain samples are obtained without any interpolation or zero-padding. These dense samples can be advantageously used for accurate parameter estimation or determination of a few principal components. The inverse discrete cosine transform can be efficiently computed from these dense, Farey-fraction transform-domain samples using the original AFT. The resulting structure is suitable for VLSI implementation.     

Operation of a synchronization system in the presence of green pulse noise

It is analytically shown that, under the action of green pulse noise on a synchronization system, the phase-locking effect is retained; however, the width of the phase-locking zone significantly depends on the pulse amplitude, whereas the character of statistics of times of random-pulse occurrences affects only slightly the synchronization process.     

小波变换和菲涅耳变换的多彩色图像加密

为了解决多彩色图像加密后,解密图像质量不佳、数据量大以及传输时速率慢的问题,采用了一种基于小波变换和菲涅耳变换的多彩色图像加密方法,加密过程中,利用小波变换的多级分解特性提取每幅彩色图像的低频分量,将低频分量分别重组为三元组图像（R,G和B）,并且依次将三元组图像（R,G和B）通过菲涅耳域中的衍射加密系统,对这3个三元组图像进一步加密,从而实现了多彩色图像的加密。结果表明,该方法不仅可以高质量地恢复原始彩色图像,而且可以同时对4幅彩色图像进行加密,提高了加密彩色图像的容量;原始图像经过小波变换,其数据量压缩到原来的1/4,有利于数据的传输和存储。该算法能够有效地同时对多幅色彩图像进行压缩和加密,不仅提高了解密图像的质量,并且具有较高的密钥敏感度和较好的鲁棒性。     

小波变换在三维面形测量中的最佳小波的选择

在几种不同的复小波函数内优选出表现最佳的小波进行小波间比较,利用连续小波变换(CWT)对同一图像进行恢复处理。通过比较不同小波的频域分布、恢复图像的效果和在恢复不同图像所得到的数据表明,复Morlet小波中的cmor1-1小波相对于其它小波在恢复图像中更具有优势。计算机模拟和实验验证了该结论的正确性和可行性。     

Suboptimal estimation of the parameters of discrete systems in the presence of correlated noise

Using an unbiased objective function and a fast algorithm which employs an iterative least-squares technique, consistent estimates are obtained for the parameters of a linear difference equation which describes a system having an output corrupted by correlated noise. The method is applied to a simulated process and compared with the generalised least-squares method.     

3-D discrete shearlet transform and video processing

In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.     

Recovering missing slices of the discrete fourier transform using ghosts

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(nlog(2)n) (for an n=N×N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT.     

Adaptive estimation of communication channel parameters in case of pulse noise presence

On a basis of mixed Markov’s process analysis in discrete time we have synthesized optimal and quasi-optimal algorithms for multi-beam communication channel in case of pulse noise presence. Analysis of quasi-optimal algorithm was carried out using example of communication system with QPSK modulation application.     

AM-FM energy detection and separation in noise using multibandenergy operators

This paper develops a multiband or wavelet approach for capturing the AM-FM components of modulated signals immersed in noise. The technique utilizes the recently-popularized nonlinear energy operator Ψ(s)=(s˙)²-ss¨ to isolate the AM-FM energy, and an energy separation algorithm (ESA) to extract the instantaneous amplitudes and frequencies. It is demonstrated that the performance of the energy operator/ESA approach is vastly improved if the signal is first filtered through a bank of bandpass filters, and at each instant analyzed (via Ψ and the ESA) using the dominant local channel response. Moreover, it is found that uniform (worst-case) performance across the frequency spectrum is attained by using a constant-Q, or multiscale wavelet-like filter bank. The elementary stochastic properties of Ψ and of the ESA are developed first. The performance of Ψ and the ESA when applied to bandpass filtered versions of an AM-FM signal-plus-noise combination is then analyzed. The predicted performance is greatly improved by filtering, if the local signal frequencies occur in-band. These observations motivate the multiband energy operator and ESA approach, ensuring the in-band analysis of local AM-PM energy. In particular, the multi-bands must have the constant-Q or wavelet scaling property to ensure uniform performance across bands. The theoretical predictions and the simulation results indicate that improved practical strategies are feasible for tracking and identifying AM-FM components in signals possessing pattern coherencies manifested as local concentrations of frequencies     

Nonlinear approach for enhancement of image focus volume in shape from focus

Mostly, shape-from-focus algorithms use local averaging using a fixed rectangle window to enhance the initial focus volume. In this linear filtering, the window size affects the accuracy of the depth map. A small window is unable to suppress the noise properly, whereas a large window oversmoothes the object shape. Moreover, the use of any window size smoothes focus values uniformly. Consequently, an erroneous depth map is obtained. In this paper, we suggest the use of iterative 3-D anisotropic nonlinear diffusion filtering (ANDF) to enhance the image focus volume. In contrast to linear filtering, ANDF utilizes the local structure of the focus values to suppress the noise while preserving edges. The proposed scheme is tested using image sequences of synthetic and real objects, and results have demonstrated its effectiveness.     

A review of the discrete Fourier transform. 2. Non-radixalgorithms, real transforms and noise

For pt.1 see ibid., vol.7, no.4, p.169-77 (1995). Since fast algorithms for the discrete Fourier transform (DFT) were first introduced thirty years ago, they have had a major impact on signal processing and are now a basic part of every electrical engineer's education. However, some of the options, and particularly the recent advances, are not as widely known as they deserve. This article, the second of two which review the fast algorithms for the DFT, looks at algorithms for transforms whose orders are not a power of two. Also discussed are ways of adapting algorithms for purely real data, the problems of fixed-point noise, and implementation options with existing hardware     

Low-complexity GMM-based block quantisation of images using the discrete cosine transform

While block transform image coding has not been very popular lately in the presence of current state-of-the-art wavelet-based coders, the Gaussian mixture model (GMM)-based block quantiser, without the use of entropy coding, is still very competitive in the class of fixed rate transform coders. In this paper, a GMM-based block quantiser of low computational complexity is presented which is based on the discrete cosine transform (DCT). It is observed that the assumption of Gaussian mixture components in a GMM having Gauss–Markov properties is a reasonable one with the DCT approaching the optimality of the Karhunen–Loève transform (KLT) as a decorrelator. Performance gains of 6–7 dB are reported over the traditional single Gaussian block quantiser at 1 bit per pixel. The DCT possesses two advantages over the KLT: being fixed and source independent, which means it only needs to be applied once; and the availability of fast and efficient implementations. These advantages, together with bitrate scalability, result in a block quantiser that is considerably faster and less complex while the novelty of using a GMM to model the source probability density function is still preserved.     

用小波变换快速求解三维电磁散射问题

在三维电磁散射问题中,用小波变换对由Ｒａｏ面片生成的阻抗矩阵进行稀疏化和求逆,比较了两种小波变换对阻抗矩阵的稀疏效果,由此指出了三维散射问题与二维散射问题中小波变换选取有所不同。通过分析和算例,表明小波变换可以有效减少阻抗矩阵的求逆时间,这对于计算电大尺寸散射体的ＲＣＳ是很有益的。     

Probability density of the phase of a random RF pulse in the presence of Gaussian noise

In this paper, we show that the probability density function (pdf) of the phase of a random nonstationary radio frequency (RF) impulse signal perturbed by Gaussian noise does not depend on the multiple time derivatives of the signal amplitude and phase at a given time instance and is the Bennett's pdf. Employing this revealing, we derive an alternative form of the conditional pdf of the phase representing it with the von Mises/Tikhonov pdf conditional on the envelope, signal-to-noise ratio (SNR), and signal phase. We expend this new form to the Fourier series and investigate for the locked and unlocked reference phases. The error probability for the phase to exceed a threshold is also analyzed.     

DCT域迭代混合的数字图像水印

提出了基于离散余弦变换和迭代混合的图像水印算法。选取图像DCT域的中频系数,对其运用迭代混合技术嵌入水印,用新的DCT系数置换原来位置的DCT系数。本系统主要包括水印的嵌入、水印的提取和水印的攻击实验三部分,其中水印图像的攻击试验又包括三种攻击试验:椒盐噪声干扰、滤波和剪切攻击,利用这三种攻击来测试水印算法的性能。仿真实验结果表明,该水印算法对于噪声干扰、滤波和剪切攻击都具有较好的鲁棒性,也是图像迭代混合思想成功应用于数字水印方面的一个例子。     

Improving power analysis attack resistance using intrinsic noise in 3D ICs

Three-dimensional (3D) integration is envisioned as a natural defense to thwart side-channel analysis (SCA) attacks on the hardware implementation of cryptographic algorithms. However, neither physical experiments nor quantitative analysis is available in existing works to study the impact of power distribution network (PDN) on the SCA attacks. Through quantitative analyses and experiments with realistic 3D models, this work demonstrates the impact of noise in PDN on the 3D chip's resilience against correlation power analysis (CPA) attack, which is one of SCA attacks. The characteristic of PDN noise is extracted from our experiments. To expand the natural defense originated from the 3D integration, this work proposes to exploit the PDN noise inherently existing in 3D chips to thwart CPA attacks. Instead of introducing external noise or flattening the power profile, the proposed method utilizes the spatially and temporally varied supply voltages from other 3D planes to blur the power correlation of the crypto unit. Both theoretical analysis and experimental validation prove that the proposed method can effectively enhance the resilience of a crypto unit embedded in the 3D chip against CPA attacks. Simulation results show the proposed method improves the average guessing entropy by 9× over the baseline. Emulation on an FPGA platform demonstrates that the proposed method successfully slows down the key retrieval speed of CPA attack, with significantly less power overhead than representable power equalization techniques. Test vector leakage assessment (TVLA) shows that the proposed method improves the confidence to accept null hypothesis 201× over the baseline.