Two-pass Algorithms Research Articles

ЛОКАЛЬНО-АДАПТИВНАЯ ФИЛЬТРАЦИЯ НЕСТАЦИОНАРНОГО ШУМА В ДЛИТЕЛЬНЫХ ЭЛЕКТРОКАРДИОГРАФИЧЕСКИХ СИГНАЛАХ

The research subject of the article is the methods of locally adaptive filtering of non-stationary (from the point of view of its variance) noise in long-term electrocardiogram (ECG) signals. The goal is to develop locally adaptive algorithms for filtering noise with different a priori unknown levels of variance in real-time for ECG signals recorded with a standard sampling rate of 500 Hz. The tasks to be solved are: to investigate the effectiveness of the developed adaptive ECG filtering algorithms using numerical statistical estimates of processing quality in a wide range of additive Gaussian noise variance variation, to investigate the suppression of real non-stationary electromyographic (EMG) noise, and to analyze the application for normal and pathological ECG signals. The methods are integral and local indicators of the filter quality according to the criteria of the mean square error and the signal-to-noise ratio was obtained using numerical simulation (via Monte Carlo analysis). The following results were obtained: an adaptive method for real-time suppression of non-stationary noise in the ECG is proposed, the one-pass and the two-pass algorithms, and the algorithm with selective depending on the preliminary estimates of noise levels re-filtering have been developed on the method basis. Statistical estimates of the filters' efficiency and analysis of their outputs show a high degree of suppression of the noise with different levels of variance in the ECGs. The distortions absence while processing QRS-complex and high efficiency of suppression of Gaussian and real EMG noise with varying variance are demonstrated. The analysis of the output signals and plots of the local adaptation parameters and the adaptable parameters of the proposed algorithms confirms the high efficiency of filtering. The developed algorithms have been successfully tested for normal and pathological ECG signals. Conclusions. The scientific novelty of the results is the development of a locally adaptive method with noise and signal-dependent filter parameters switching and of the adaptive algorithms based on this method for non-stationary noise reduction in the ECG in real-time. This method does not require time for filter parameters adaptation and a priori information about the noise variance, and it has a high-speed performance in real-time mode.

Temporal paths discovery with multiple constraints in attributed dynamic graphs

Temporal path discovery in dynamic graphs is significant in many applications, such as the trip planning in transportation networks, and the disease progression tracking in gene networks. Attributed Dynamic Graph (ADG) contains multiple value-changed attributes on edges, such as the speed of a bus between two stations, and the price of the bus ticket in different time periods. The traditional methods for temporal path discovery in ADGs assume users only consider a single constraint on the attributes in their models, such as finding the fast route to reach the destination under the constraint of a given budget, which makes the path discovery problem simple though it still suffers expensive time cost. However, such an assumption is too strict in real applications, where users can specify multiple constraints, such as finding the fast route under the constraints of a given budget and the total number of stopovers. In such a situation, the temporal path discovery becomes more complicated as it subsumes the classical NP-Complete Multi-Constraint Path (MCP) problem, and thus the traditional methods cannot work for finding a new type of Temporal Path with Multiple Constraints (TPMC). In this paper, we propose a set of new Two-Pass approximation algorithms to bi-directionally search ADGs to find TPMC results. To the best of our knowledge, our Two-Pass algorithms are the first algorithms to support the discovery of the temporal paths with multiple constraints in ADGs. The experimental results on 12 real-world dynamic graphs demonstrate that our algorithms outperform the state-of-the-art methods in both efficiency and effectiveness.

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

Modeling full-length video using Markov-modulated Gamma-based framework

All traffic models for MPEG-like encoded variable bit rate (VBR) video can be broadly categorized into (1) data-rate models (DRMs) and (2) frame-size models (FSMs). Almost all proposed VBR traffic models are DRMs. DRMs generate only data arrival rate, and are good for estimating average packet-loss and ATM buffer overflowing probabilities, but fail to identify such details as percentage of frames affected. FSMs generate sizes of individual MPEG frames, and are good for studying frame loss rate in addition to data loss rate. Among three previously proposed FSMs: (1) one generates frame sizes for full-length movies without preserving group-of-pictures (GOP) periodicity; (2) one generates VBR video traffic for news videos from scene content description provided to it; and (3) one generates frame sizes for full-length movies without preserving size-based video-segment transitions. We propose two FSMs that generate frame sizes for full-length VBR videos preserving both GOP periodicity and size-based video-segment transitions. First, two-pass algorithms for analysis of full-length VBR videos are presented. After two-pass analysis, these algorithms identify size-based classes of video shots into which the GOPs are partitioned. Frames in each class produce three data sets, one each for I-, B-, and P-type frames. Each of these data sets is modeled with an axis-shifted gamma distribution. Markov renewal processes model (size-based) video segment transitions. We have used quartile-quartile (QQ) plots to show visual similarity of model-generated VBR video data sets with original data set. Leaky-bucket simulation study has been used to show similarity of data and frame loss rates between model-generated VBR videos and original video. Our study of frame-based VBR video revealed that even a low data-loss rate could affect a large fraction of I frames, causing a significant degradation of the quality of transmitted video.

Radiosity for scenes with many mirror reflections

This paper introduces an effective and efficient approach to synthesize images of environments with many mirror reflections. According to existing two-pass algorithms for non-perfectly diffuse environments, the computational complexity increases in proportion to the number of mirror reflections. We propose an improved two-pass algorithm based on a reflection tree data structure to manage complicated energy interactions due to interreflections of multiple mirrors. Techniques in radiosity computation such as progressive refinement and hierarchical radiosity, and techniques in visibility computation such as bounding volume hierarchy, are used to accelerate the computation of the first pass. In the second pass, a multilayered clip-and-paste method is introduced to replace the time-consuming ray tracing method. In addition, problems and solutions in realizing multilayered clip-and-paste are also addressed. The complexity of the proposed algorithm is analyzed. Empirical tests are given and shown to be in accord with the analysis.

Recursive binary dilation and erosion using digital line structuring elements in arbitrary orientations

Performing morphological operations such as dilation and erosion of binary images, using very long line structuring elements is computationally expensive when performed brute-force following definitions. We present two-pass algorithms that run at constant time for obtaining binary dilations and erosions with all possible length line structuring elements, simultaneously. The algorithms run at constant time for any orientation of the line structuring element. Another contribution of this paper is the use of the concept of orientation error between a continuous line and its discrete counterpart. The orientation error is used in determining the minimum length of the basic digital line structuring element used in obtaining what we call dilation and erosion transforms. The transforms are then thresholded by the length of the desired structuring element to obtain the dilation and erosion results. The algorithms require only one maximum operation for erosion transform and only one minimum operation for dilation transform, and one thresholding step and one translation step per result pixel. We tested the algorithms on Sun Sparc Station 10, on a set of 240x250 salt and pepper noise images with probability of a pixel being a 1-pixel set to 0.25, for orientations of the normals of the structuring elements in the range [pi/2,3pi/2] and lengths, in pixels, in the range [5,145]. We achieved a speed up of about 50 (and for special orientations theta in {(pi/2), (3pi/4), pi, (5pi/4), (3pi/2)} a speed up of about 100) when the structuring elements had lengths of 145 pixels, over the brute-force methods in these experiments. We compared the results of our dilation algorithm with those of the algorithm discussed by Soille et al. (see IEEE Trans. Pattern Anal. Machine Intell., vol.18, p.562-67, 1996) and showed that for binary dilation (and erosion since it is just the dilation of the background with the reflected structuring element) our algorithm performed better and achieved a speed up of about four when dilation or erosion transform alone is obtained.

Modulus quantization for matching-pursuit video coding

Overcomplete signal decomposition using matching pursuits has been shown to be an efficient technique for coding motion-residual images in a hybrid video coder. Unlike orthogonal decomposition, matching pursuit uses an in-the-loop modulus quantizer which must be specified before coding begins. This complicates the quantizer design, since the optimal quantizer depends on the statistics of the matching-pursuit coefficients which in turn depend on the in loop quantizer actually used. In this paper, we address the modulus quantizer design issue, specifically developing frame-adaptive quantization schemes for the matching-pursuit video coder. Adaptive dead-zone subtraction is shown to reduce the information content of the modulus source, and a uniform threshhold quantizer is shown to be optimal for the resulting source. Practical two-pass and one-pass algorithms are developed to jointly determine the quantizer parameters and the number of coded basis functions in order to minimize coding distortion for a given rate. The compromise one-pass scheme performs nearly as well as the full two-pass algorithm, but with the same complexity as a fixed-quantizer design. The adaptive schemes are shown to outperform the fixed quantizer used in earlier works, especially at high bit rates, where the gain is as high as 1.7 dB.

Fast direct Fourier methods, based on one- and two-pass coordinate transformations, yield accurate reconstructions of x-ray CT clinical images

The conversion from polar to Cartesian coordinates can be carried out with two-pass algorithms. The paper describes two different methods based on concentric square frames and octagonal frames and their results, obtained with accurate interpolations based on the `moving window Shannon reconstruction' (MWSR). The embedding of these algorithms in direct Fourier methods (DFMs) of tomographic reconstruction is discussed. With respect to one-pass methods and to the use of octagonal frames, the square frame method makes it possible to carry out the first pass, a radial resampling, in the direct space, before computing 1D Fourier transforms (FTs) of projections. Reconstructions of clinical images from the raw data of a third-generation x-ray tomograph are presented and compared with those obtained with one-pass DFMs and with the convolution back-projection method (CBPM) performed by the instrument. The simple algorithm using square frames yields results in complete agreement with other DFM protocols and the CBPM. On a general-purpose computer, the execution of DFM protocols based on one-pass and two-pass coordinate transformations is 35 to 55 times faster than the CBPM and make the algorithms attractive for modern instrumentation.

On the methods for solving Yule-Walker equations

The three well-known fast algorithms for the solution of Yule-Walker equations-the Levinson, Euclidean, and Berlekamp-Massey algorithms-are reviewed, and the relationship between each of them and the Pade approximation problem is shown. The algorithms are classified with reference to three criteria, namely: (1) the path they follow in the Pade table; (2) the organization of the computations (one-pass or two-pass); and (3) the auxiliary variables used. This classification shows that the set of known classical algorithms is not complete, and the missing variants are proposed. With these variants of the Berlekamp-Massey and Euclid algorithms, both forward and backward predictors can be obtained without additional cost. A unified representation of the two-pass algorithms is given in such a way that the application of the divide and conquer strategy becomes straightforward. A general doubling algorithm which represents all the associated doubling algorithms in an exhaustive way is provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comparison of Several Algorithms for Computing Sample Means and Variances

Abstract Several one-pass and two-pass algorithms for the computation of sample means and variances are compared by their performance on sets of randomly generated data and systematically generated data with random noise. The relation between the performance of each algorithm and the coefficient of variation of the population from which random data sets are generated is explored.