Wavelet thresholding of multivalued images

In this paper, a denoising technique for multivalued images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients. Specific functions of the wavelet coefficients are defined that exploit interscale and/or interband correlation of the signal. Three functions are studied: the square of the wavelet coefficients, products of coefficients at adjacent scales, and products of coefficients from different bands. For these functions, the signal and noise probability density functions (pdf) become more separated. The high signal correlation between bands is exploited by summing these products over all bands, in this way separating noise and signal pdfs even more. The noise pdf of the proposed quantities is derived analytically and from this, a wavelet threshold is derived. The technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images and on multimodal MRI images.     

A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration.

Iterative shrinkage/thresholding (IST) algorithms have been recently proposed to handle a class of convex unconstrained optimization problems arising in image restoration and other linear inverse problems. This class of problems results from combining a linear observation model with a nonquadratic regularizer (e.g., total variation or wavelet-based regularization). It happens that the convergence rate of these IST algorithms depends heavily on the linear observation operator, becoming very slow when this operator is ill-conditioned or ill-posed. In this paper, we introduce two-step IST (TwIST) algorithms, exhibiting much faster convergence rate than IST for ill-conditioned problems. For a vast class of nonquadratic convex regularizers (l(p) norms, some Besov norms, and total variation), we show that TwIST converges to a minimizer of the objective function, for a given range of values of its parameters. For noninvertible observation operators, we introduce a monotonic version of TwIST (MTwIST); although the convergence proof does not apply to this scenario, we give experimental evidence that MTwIST exhibits similar speed gains over IST. The effectiveness of the new methods are experimentally confirmed on problems of image deconvolution and of restoration with missing samples.     

Wavelet shrinkage and generalized cross validation for imagedenoising

We present a denoising method based on wavelets and generalized cross validation and apply these methods to image denoising. We describe the method of modified wavelet reconstruction and show that the related shrinkage parameter vector can be chosen without prior knowledge of the noise variance by using the method of generalized cross validation. By doing so, we obtain an estimate of the shrinkage parameter vector and, hence, the image, which is very close to the best achievable mean-squared error result-that given by complete knowledge of the underlying clean image.     

Multitaper power spectrum estimation and thresholding: wavelet packets versus wavelets

It was suggested that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a wavelet packet tree to the log multitaper spectrum ordinates, thresholding the empirical wavelet packet coefficients, and then inverting the transform. For a small number of tapers, suitable transforms/partitions for the logarithm of the multitaper spectrum estimator are derived using a method matched to statistical thresholding properties. The partitions thus derived starting from different stationary time series are all similar and easily derived, and any differences between the wavelet packet and discrete wavelet transform (DWT) approaches are minimal. For a larger number of tapers, where the chosen parameters satisfy the conditions of a proven theorem, the simple DWT again emerges as appropriate. Hence, using our approach to thresholding and the method of partitioning, we conclude that the DWT approach is a very adequate wavelet-based approach and that the use of wavelet packets is unnecessary.     

Unsupervised image thresholding: hardware architecture and its usage for FPGA-SoC platform

ABSTRACT

Otsu’s global automatic image thresholding operation is used in various image processing applications. It needs computation of normalized cumulative histogram, mean and cumulative moments that are compute-intensive operations. In this paper, a custom architecture is presented for an efficient computation of Otsu’s algorithm along with its utilization as an intellectual property (IP) core in a field programmable gate array (FPGA) based system-on-chip (SoC) environment for the application of connected component analysis (CCA). A self-normalization technique is employed, where single-cycle, read–modify–write operations are performed with block random access memories (BRAMs) and digital signal processing (DSP)slices. The architecture is designed for 640 × 480 size of images that are captured by a high-resolution analouge camera and buffered in a DDR2 SDRAM of Xilinx ML-507 platform at 25.175 MHz clock frequency. The embedded PowerPC processor core is used to control the frame acquisition process. Experimental results on Virtex-5 xc5vfx70t FPGA device show that the architecture utilizes 1.4% slices, 2.7% BRAMs and 3.9% DSP48E slices. The total power consumption of the design is 1440.59 mW. The proposed architecture as an IP core is able to work in real-time with standard VGA resolution video and requires low computational resources.     

Quantitative design and evaluation of enhancement/thresholding edge detectors

Quantitative design and performance evaluation techniques are developed for the enhancement/thresholding class of image edge detectors. The design techniques are based on statistical detection theory and deterministic pattern-recognition classification procedures. The performance evaluation methods developed include: a)deterministic measurement of the edge gradient amplitude; b)comparison of the probabilities of correct and false edge detection; and c) figure of merit computation. The design techniques developed are used to optimally design a variety of small and large mask edge detectors. Theoretical and experimental comparisons of edge detectors are presented.     

Automatic selection and fusion of color spaces for image thresholding

Automatic selection of color models has a great significance for machine vision purposes like image segmentation, object recognition, etc. Typically, selection of a proper color model is a problem that can just solve by testing the models on the target one by one. To achieve a proper color model, in this article, we propose a new method which is shaped on the basis of clustering and relation among models. The proposed method is verified experimentally for two different images (in thresholding purpose). The experimental results show that this method has a suitable power for automatic purposes.     

Survey and comparative analysis of entropy and relative entropy thresholding techniques

Entropy-based image thresholding has received considerable interest in recent years. Two types of entropy are generally used as thresholding criteria: Shannon's entropy and relative entropy, also known as Kullback-Leibler information distance, where the former measures uncertainty in an information source with an optimal threshold obtained by maximising Shannon's entropy, whereas the latter measures the information discrepancy between two different sources with an optimal threshold obtained by minimising relative entropy. Many thresholding methods have been developed for both criteria and reported in the literature. These two entropy-based thresholding criteria have been investigated and the relationship among entropy and relative entropy thresholding methods has been explored. In particular, a survey and comparative analysis is conducted among several widely used methods that include Pun and Kapur's maximum entropy, Kittler and Illingworth's minimum error thresholding, Pal and Pal's entropy thresholding and Chang et al.'s relative entropy thresholding methods. In order to objectively assess these methods, two measures, uniformity and shape, are used for performance evaluation     

GRASP: basic components and enhancements

GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution is found. While, in general, the construction phase of GRASP is a randomized greedy algorithm, other types of construction procedures have been proposed. Repeated applications of a construction procedure yields diverse starting solutions for the local search. This paper gives an overview of GRASP describing its basic components and enhancements to the basic procedure, including reactive GRASP and intensification strategies.     

Wavelet and subband transforms: fundamentals and communicationapplications

Subband and wavelet transforms have been a subject of great interest, especially in the fields of signal processing and applied mathematics. This article presents a tutorial on this subject, emphasizing the fundamentals and the reason for its success, importance, and potential. Subband and wavelet transform applications in communications are also reviewed. These application areas include interference excision, spread spectrum codes based on subband transform bases, CDMA, and discrete multitone transceivers     

Joint thresholding and quantizer selection for transform imagecoding: entropy-constrained analysis and applications to baseline JPEG

Striving to maximize baseline (Joint Photographers Expert Group-JPEG) image quality without compromising compatibility of current JPEG decoders, we develop an image-adaptive JPEG encoding algorithm that jointly optimizes quantizer selection, coefficient "thresholding", and Huffman coding within a rate-distortion (R-D) framework. Practically speaking, our algorithm unifies two previous approaches to image-adaptive JPEG encoding: R-D optimized quantizer selection and R-D optimal thresholding. Conceptually speaking, our algorithm is a logical consequence of entropy-constrained vector quantization (ECVQ) design principles in the severely constrained instance of JPEG-compatible encoding. We explore both viewpoints: the practical, to concretely derive our algorithm, and the conceptual, to justify the claim that our algorithm approaches the best performance that a JPEG encoder can achieve. This performance includes significant objective peak signal-to-noise ratio (PSNR) improvement over previous work and at high rates gives results comparable to state-of-the-art image coders. For example, coding the Lena image at 1.0 b/pixel, our JPEG encoder achieves a PSNR performance of 39.6 dB that slightly exceeds the quoted PSNR results of Shapiro's wavelet-based zero-tree coder. Using a visually based distortion metric, we can achieve noticeable subjective improvement as well. Furthermore, our algorithm may be applied to other systems that use run-length encoding, including intraframe MPEG and subband or wavelet coding.     

Vector space framework for unification of one- and multidimensionalfilter bank theory

A number of results in filter bank theory can be viewed using vector space notations. This simplifies the proofs of many important results. In this paper, we first introduce the framework of vector space, and then use this framework to derive some known and some new filter bank results as well. For example, the relation among the Hermitian image property, orthonormality, and the perfect reconstruction (PR) property is well-known for the case of one-dimensional (1-D) analysis/synthesis filter banks. We can prove the same result in a more general vector space setting. This vector space framework has the advantage that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case. Many results in 1-D filter bank theory are hence extended to the multidimensional case, with some algebraic manipulations of integer matrices. Some examples are: the equivalence of biorthonormality and the PR property, the interchangeability of analysis and synthesis filters, the connection between analysis/synthesis filter banks and synthesis/analysis transmultiplexers, etc. Furthermore, we obtain the subband convolution scheme by starting from the generalized Parseval's relation in vector space. Several theoretical results of wavelet transform can also be derived using this framework. In particular, we derive the wavelet convolution theorem     

小波分析和小波包在图像消噪中的应用

小波包理论是在小波基础上发展起来的时频分析理论,在图像消噪中取得了较好的应用。文中介绍了小波分析和小波包的基本理论,分析了基于小波和小波包进行图像消噪的方法,利用MATLAB7对相同舍噪图像进行了计算机仿真,并对仿真结果进行了分析。实验表明,图像消噪效果与阈值的选取密切相关,小波包消噪后的效果比小波更好。     

多年鼎足,今朝一统--国家信息安全产品认证管理委员会成立

我国信息安全产品认证管理委员会的成立,标志着建立统一的信息安全认证认可体系的工作进入了实质性的实施阶段。有关高层主管纵论统一认证认可的意义、目标和希望,并勾勒出五年发展的大体框架。     

The unification of differential encoding and decoding algorithm for various signals

Many monographs point out that differential encoding and decoding is necessary for ef- fectual information transmission against phase ambiguity while seldom discuss the reason why phase ambiguity will emerge inevitably.Available algorithms are specially designed for certain modulation scheme;these algorithms cannot satisfy the requirement of soft-defined radio,which perhaps demands a uniform algorithm for different modulations.This paper proposes a new opinion on phase ambiguity from the view of probability.This opinion believes that modulating symbol sequence can affect,at optimum sampling epoch,the modulated waveform as oscillating carrier has done,and so the stochastic sequence leads to phase ambiguity.Based on a general signal model,this paper also puts forward a novel universal algorithm,which is suitable for different signals,even some new ones,by configuring several parameters.     

A unification of network coding and tree-packing (routing) theorems

Given a network of lossless links with rate constraints, a source node, and a set of destination nodes, the multicast capacity is the maximum rate at which the source can transfer common information to the destinations. The multicast capacity cannot exceed the capacity of any cut separating the source from a destination; the minimum of the cut capacities is called the cut bound. A fundamental theorem in graph theory by Edmonds established that if all nodes other than the source are destinations, the cut bound can be achieved by routing. In general, however, the cut bound cannot be achieved by routing. Ahlswede et al. established that the cut bound can be achieved by performing network coding, which generalizes routing by allowing information to be mixed. This paper presents a unifying theorem that includes Edmonds' theorem and Ahlswede et al.'s theorem as special cases. Specifically, it shows that the multicast capacity can still be achieved even if information mixing is only allowed on edges entering relay nodes. This unifying theorem is established via a graph theoretic hardwiring theorem, together with the network coding theorems for multicasting. The proof of the hardwiring theorem implies a new proof of Edmonds' theorem.     

T-MPLS统一多业务适配及其OPNET建模

讨论了T-MPLS(transport multi-protocol label.switching)统一多业务适配的必要性,并结合T-MPLS网络的特点,设计了针对不同业务的适配算法.阐述了利用OPNET对T-MPLS多业务进行适配的建模思想和处理过程,对模型的可行性及优势进行了分析.     

Adaptive Morphological Representation of Signals: Polynomial and Wavelet Methods

In this paper, we propose a novel signal representation based on mathematical morphology, and with it develop representations analogous to the polynomial transform and the bank-of-filters implementation of the wavelet representation. The geometric decomposition of a signal is achieved by separating it into analysis frames and applying mathematical morphological operators with adaptive structuring functions to each frame. The adaptation parameters are found by solving iteratively nonlinear equations that result from constraining the morphological results to achieve optimal fitting. If the structuring functions are derived from real-valued orthogonal polynomials defined on a window, the representation is analogous to the polynomial transform. Using a morphological interpolation, we derive a pyramid-like structure to decompose a signal into gross and fine information components, at different scales, just as in the wavelet transformation. Non-linear morphological operators reduce the computational complexity of the proposed representations. Although these representations are easily extended to two-dimensions, one needs to consider the non–unique ordering of the structuring functions, and the different sampling, decimation and interpolation procedures in two-dimensions. The application of our procedures is mainly in image data compression, but they could also used in object identification. We illustrate our representations by means of one- and two-dimensional examples.