Detecting computer-induced errors in remote-sensing JPEG compression algorithms.

The JPEG image compression standard is very sensitive to errors. Even though it contains error resilience features, it cannot easily cope with induced errors from computer soft faults prevalent in remote-sensing applications. Hence, new fault tolerance detection methods are developed to sense the soft errors in major parts of the system while also protecting data across the boundaries where data flow from one subsystem to the other. The design goal is to guarantee no compressed or decompressed data contain computer-induced errors without detection. Detection methods are expressed at the algorithm level so that a wide range of hardware and software implementation techniques can be covered by the fault tolerance procedures while still maintaining the JPEG output format. The major subsystems to be addressed are the discrete cosine transform, quantizer, entropy coding, and packet assembly. Each error detection method is determined by the data representations within the subsystem or across the boundaries. They vary from real number parities in the DCT to bit-level residue codes in the quantizer, cyclic redundancy check parities for entropy coding, and packet assembly. The simulation results verify detection performances even across boundaries while also examining roundoff noise effects in detecting computer-induced errors in processing steps.     

基于离散余弦变换的图像压缩研究

图像压缩是数据压缩技术在数字图像上的应用,其目的是减少图像数据中的冗余信息,从而用更加高效的格式存储和传输数据。图像压缩可以是有损数据压缩也可以是无损数据压缩。这里所研究的是有损压缩技术,对于此类技术,变换编码是最常用的方法,如离散余弦变换（DCT）或者小波变换这样的傅里叶相关变换,然后进行量化和用熵编码法压缩。     

Lossy-to-lossless compression of medical volumetric data using three-dimensional integer wavelet transforms

We study lossy-to-lossless compression of medical volumetric data using three-dimensional (3-D) integer wavelet transforms. To achieve good lossy coding performance, it is important to have transforms that are unitary. In addition to the lifting approach, we first introduce a general 3-D integer wavelet packet transform structure that allows implicit bit shifting of wavelet coefficients to approximate a 3-D unitary transformation. We then focus on context modeling for efficient arithmetic coding of wavelet coefficients. Two state-of-the-art 3-D wavelet video coding techniques, namely, 3-D set partitioning in hierarchical trees (Kim et al., 2000) and 3-D embedded subband coding with optimal truncation (Xu et al., 2001), are modified and applied to compression of medical volumetric data, achieving the best performance published so far in the literature-both in terms of lossy and lossless compression.     

快速傅里叶变换对信号频谱的简单分析

快速傅里叶变换(FFT)是离散傅里叶变换(DFT)的快速算法,广泛运用于故障诊断领域,因每种故障的频率成分不同,FFT可以根据这些独有的频率成分检测出不同的故障来。同时快速傅里叶变换还应用于控制工程、图像处理、机床生产、数据采集和雷达探测等方面,对社会中的工业发展起到很大的作用。本文就FFT对信号的频谱做出简单分析,对不同采样点数进行相应频谱判断,找出理论与频率图像出现误差的原因,以便人们对FFT技术能够进行更好的使用。     

Quadtree and symmetry in FFT computation of digital images

The discrete Fourier transform (DFT) of a real sequence f[x, y] of size N×N, where N=2ⁿ, can be computed by a two-dimensional (2-D) FFT of size N/4, or smaller if f[x, y] is known to have certain symmetries. This paper presents theorems that identify the symmetry in f[x, y] based on the depth of the quadtree to expedite 2-D FFT computation of coherent digital images. In principle, it establishes that if the quadtree of f[x, y] has maximum depth kn , then the DFT can be computed by a 2-D FFT of size K/2. An algorithm is given, and its performance analyzed. Finally, applications are considered in transform coding systems and lossy compression of images     

Arithmetic coding algorithm with embedded channel coding

A joint lossless source and channel coding approach that incorporates error detection and correction capabilities in arithmetic coding is exploited. The encoded binary data representation allows the source decoder to recover the source symbols, even with channel errors. The self-synchronisation property of arithmetic coding, the knowledge of the source statistics, and some added redundancy are used for error detection and correction     

Time-domain analysis of lossy multiconductor transmission lines based on the Lax–Wendroff technique

Taking advantage of the hyperbolic characteristics of the telegrapher equations, this paper applies the Lax–Wendroff technique, usually used in fluid dynamics, to transmission line analysis. A second-order-accurate Lax–Wendroff difference scheme for the telegrapher equations for both uniform and nonuniform transmission lines is derived. Based on this scheme, a new method for analyzing lossy multiconductor transmission lines which do not need to be decoupled is presented by combining with matrix operations. Using numerical experiments, the proposed method is compared with the characteristic method, the fast Fourier transform (FFT) approach, and the Lax–Friedrichs technique. With the presented method, a circuit including lossy multiconductor transmission lines is analyzed and the results are consistent with those of PSPICE. The nonlinear circuit including nonuniform lossy multiconductor transmission lines is also computed and the results are verified by HSPICE. The proposed method can be conveniently applied to either linear or nonlinear circuits which include general transmission lines, and is proved to be efficient.     

The generalized method of characteristics for waveform relaxationanalysis of lossy coupled transmission lines

The transient response of lossy coupled transmission lines is simulated by iterative waveform relaxation analyses of equivalent disjoint networks constructed with congruence transformers, fast Fourier transform (FFT) waveform generators, and characteristic impedances synthesized by the Pade approximation. A two order reduction of CPU time and one order savings in computer memory are achieved. A lossy directional coupler is simulated for illustration     

多载波中的实数FFT及其离散Hartley变换实现

在OFDM／DMT多载波调制中，FFT为实数FFT（Real—Valued FFT），输入全部为实数，变换后的输出为偶函数即具有一定的共轭特性。相应地，IFFT为实数FFT的逆过程。实数FFT的实现与复数FFT具有很大的不同，文中提出了一种基于离散Hartley变换的实现方法，运算过程全部为实数过程，与复数FFT相比，所需的乘法、加法运算以及RAN的开销均大幅度降低。     

Decoding real-number convolutional codes: change detection, Kalmanestimation

Convolutional codes which employ real-number symbols are difficult to decode because of the size of the alphabet and the numerical and roundoff noise inherent in arithmetic operations. Such codes find applications in both channel coding for communication systems and in fault-tolerance support for signal processing subsystems. A new method for error correction based on optimum mean-square recursive Kalman estimation techniques incorporates time-varying models for the system and associated disruptive noise sources. The underlying common model for communications and fault tolerance applications assumes the system operates nominally with low levels of channel or numerical and roundoff noise, occasionally experiencing temporarily larger noise statistics. A time-varying Kalman estimation structure which uses single-step and fixed-lag smoothing predictors can correct errors to within the nominal low-noise levels. Correction actions may be activated only when larger activity is detected, so methods for detecting possible error situations are developed. However, misdetection is not a serious problem because the Kalman correction methods only track significant errors in the data. Two activity detection techniques are examined; one is based on likelihood ratio tests while another uses clipped samples and binary pattern matching. Several examples showing simulated mean-square error performance and decoded waveforms from error injection experiments are presented     

An image multiresolution representation for lossless and lossycompression

We propose a new image multiresolution transform that is suited for both lossless (reversible) and lossy compression. The new transformation is similar to the subband decomposition, but can be computed with only integer addition and bit-shift operations. During its calculation, the number of bits required to represent the transformed image is kept small through careful scaling and truncations. Numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity. In addition, we propose entropy-coding methods that exploit the multiresolution structure, and can efficiently compress the transformed image for progressive transmission (up to exact recovery). The lossless compression ratios are among the best in the literature, and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods.     

FFT算法在OFDM中的应用研究与设计

针对当前高速数据传输技术中多径效应,符号间干扰的缺陷,提出了正交频分复用（OFDM）系统的设计方案。该方案利用快速傅里叶变换FFT实现调制和解调。这里以Quartus Ⅱ为平台用VHDL语言编程实现各模块,设计了FFT处理器。通过综合仿真和时序分析与MATLAB仿真结果比较验证其正确可行。该系统可以解决高速信息流在信道中的传输问题,可以有效地对抗多径效应,消除符号间干扰,实现数据的高速传输。     

Low noise reversible MDCT (RMDCT) and its application in progressive-to-lossless embedded audio coding

A reversible transform converts an integer input to an integer output, while retaining the ability to reconstruct the exact input from the output sequence. It is one of the key components for lossless and progressive-to-lossless audio codecs. In this work, we investigate the desired characteristics of a high-performance reversible transform. Specifically, we show that the smaller the quantization noise of the reversible modified discrete cosine transform (RMDCT), the better the compression performance of the lossless and progressive-to-lossless codec that utilizes the transform. Armed with this knowledge, we develop a number of RMDCT solutions. The first RMDCT solution is implemented by turning every rotation module of a float MDCT (FMDCT) into a reversible rotation, which uses multiple factorizations to further reduce the quantization noise. The second and third solutions use the matrix lifting to implement a reversible fast Fourier transform (FFT) and a reversible fractional-shifted FFT, respectively, which are further combined with the reversible rotations to form the RMDCT. With the matrix lifting, we can design the RMDCT that has less quantization noise and can still be computed efficiently. A progressive-to-lossless embedded audio codec (PLEAC) employing the RMDCT is implemented with superior results for both lossless and lossy audio compression.     

Effects of finite register length in digital filtering and the fast Fourier transform

When digital signal processing operations are implemented on a computer or with special-purpose hardware, errors and constraints due to finite word length are unavoidable. The main categories of finite register length effects are errors due to A/D conversion, errors due to roundoffs in the arithmetic, constraints on signal levels imposed by the need to prevent overflow, and quantization of system coefficients. The effects of finite register length on implementations of linear recursive difference equation digital filters, and the fast Fourier transform (FFT), are discussed in some detail. For these algorithms, the differing quantization effects of fixed point, floating point, and block floating point arithmetic are examined and compared. The paper is intended primarily as a tutorial review of a subject which has received considerable attention over the past few years. The groundwork is set through a discussion of the relationship between the binary representation of numbers and truncation or rounding, and a formulation of a statistical model for arithmetic roundoff. The analyses presented here are intended to illustrate techniques of working with particular models. Results of previous work are discussed and summarized when appropriate. Some examples are presented to indicate how the results developed for simple digital filters and the FFT can be applied to the analysis of more complicated systems which use these algorithms as building blocks.     

Improved Accuracy Factors for the Nonuniform Fast Fourier Transform (NUFFT) Algorithm

Based on the regular Fourier matrix, a new set of accuracy factors is proposed for the nonuniform fast Fourier transform algorithm to improve the accuracy of transformed data. It shows that the proposed factors can reduce the errors by three to more than ten times with almost the same number of arithmetic operations. Numerical examples are shown for the applications in computational electromagnetics.     

基于IWT和FCM的曲线矢量数据压缩方法

矢量数据压缩对于GIS数据的存储、网络传输以及在移动设备中的使用都具有重要意义。在此通过对曲线矢量数据特点的分析,提出基于整数小波变换的矢量数据压缩方法。压缩方案包括3个主要流程：矢量数据整型化。曲线矢量数据具有相邻坐标点间坐标值大小差别不大的特点,将坐标点间的差值转换为整型的偏移量,用偏移量表示矢量数据的坐标点,利用整数小波变换处理偏移量序列。实验表明,偏移量序列经过整数小波变换得到的小波系数序列在空间分布上更加集中,适合使用高效的编码压缩方法;对变换后的小波系数进行编码压缩。在此使用模糊C均值聚类字典法编码实现了曲线矢量数据的有损编码。通过实验和其他压缩算法结果的对比,该方法具有压缩比较高,失真小的特点。     

Synthetic aperture radar image compression using tree-structured edge-directed orthogonal wavelet packet transform

Currently, wavelet-based coding algorithms are popular for synthetic aperture radar (SAR) image compression, which is very important for reducing the cost of data storage and transmission in relatively slow channels. However, standard wavelet transform is limited by spatial isotropy of its basis functions that is not completely adapted to represent image entities like edges or textures, which means wavelet-based coding algorithms are suboptimal to image compression. In this paper, a novel tree-structured edge-directed orthogonal wavelet packet transform is proposed for SAR image compression. Inspired by the intrinsic geometric structure of images, the new transform improves the performance of standard wavelet by filtering along the regular direction first and then along the orthogonal direction with directional lifting structure. The cost function of best basis selection is designed by textural and directional information for tree-structured edge-directed orthogonal wavelet packet transform. The new transform including speckle reduction can be used to construct SAR image coder with the embedded block coding with optimal truncation for transform coefficients, and arithmetic coding for additional information. The experimental results show that the proposed approach outperforms JPEG2000 and Fast wavelet packet (FWP), both visually and item of PSNR values.     

MODIS多光谱图像压缩研究

为有效存储MODIS多光谱图像数据,该文提出一种基于谱间预测和整数小波变换的多光谱图像压缩算法.首先通过构造谱间最优预测器去除谱间冗余,再利用整数小波变换和SPIHT算法对预测误差图像去除空间冗余,最后进行自适应算术编码.该方法可实现MODIS多光谱图像的无损、近无损和有损压缩,取得了满意的实验结果;在不同小波基条件下与3D-SPIHT算法比较,表明了该方法的有效性.     

Lossless, near-lossless, and refinement coding of bilevel images

We present general and unified algorithms for lossy/lossless coding of bilevel images. The compression is realized by applying arithmetic coding to conditional probabilities. As in the current JBIG standard the conditioning may be specified by a template. For better compression, the more general free tree may be used. Loss may be introduced in a preprocess on the encoding side to increase compression. The primary algorithm is a rate-distortion controlled greedy flipping of pixels. Though being general, the algorithms are primarily aimed at material containing half-toned images as a supplement to the specialized soft pattern matching techniques that work better for text. Template based refinement coding is applied for lossy-to-lossless refinement. Introducing only a small amount of loss in half-toned test images, compression is increased by up to a factor of four compared with JBIG. Lossy, lossless, and refinement decoding speed and lossless encoding speed are less than a factor of two slower than JBIG. The (de)coding method is proposed as part of JBIG2, an emerging international standard for lossless/lossy compression of bilevel images.     

A wavelet-based two-stage near-lossless coder.

In this paper, we present a two-stage near-lossless compression scheme. It belongs to the class of "lossy plus residual coding" and consists of a wavelet-based lossy layer followed by arithmetic coding of the quantized residual to guarantee a given L(infinity) error bound in the pixel domain. We focus on the selection of the optimum bit rate for the lossy layer to achieve the minimum total bit rate. Unlike other similar lossy plus lossless approaches using a wavelet-based lossy layer, the proposed method does not require iteration of decoding and inverse discrete wavelet transform in succession to locate the optimum bit rate. We propose a simple method to estimate the optimal bit rate, with a theoretical justification based on the critical rate argument from the rate-distortion theory and the independence of the residual error.