George Carayannis

A fast sequential algorithm for least-squares filtering and prediction

A new computationally efficient algorithm for sequential least-squares (LS) estimation is presented in this paper. This fast a posteriori error sequential technique (FAEST) requires 5p MADPR (multiplications and divisions per recursion) for AR modeling and 7p MADPR for LS FIR filtering, where p is the number of estimated parameters. In contrast the well-known fast Kalman algorithm requires 8p MADPR for AR modeling and 10p MADPR for FIR filtering. The increased computational speed of the introduced algorithm stems from an alternative definition of the so-called Kalman gain vector, which takes better advantage of the relationships between forward and backward linear prediction.

Speech enhancement from noise: a regenerative approach

Abstract In this paper a speech enhancement technique is proposed based on principal component analysis and a new criterion for the selection of the parsimonious number of components for noise-free signal regeneration. Both isolated phonemes and continuous speech experiments are presented. The results have been evaluated by informal listening and SNR computations, which show that the methodology has an improved performance compared to existing techniques.

Handwritten document image segmentation into text lines and words

Two novel approaches to extract text lines and words from handwritten document are presented. The line segmentation algorithm is based on locating the optimal succession of text and gap areas within vertical zones by applying Viterbi algorithm. Then, a text-line separator drawing technique is applied and finally the connected components are assigned to text lines. Word segmentation is based on a gap metric that exploits the objective function of a soft-margin linear SVM that separates successive connected components. The algorithms tested on the benchmarking datasets of ICDAR07 handwriting segmentation contest and outperformed the participating algorithms.

Fast recursive algorithms for a class of linear equations

In many signal processing applications, one often seeks the solution of a linear system of equations by means of fast algorithms. The special form of the matrix associated with the linear system may permit the development of algorithms requiring 0 (p2) or fewer operations. Hankel and Toeplitz matrices provide well known examples and various fast schemes have been developed in the literature to cover these cases. These techniques have common characteristics so that they may be generalized to cover a wider class of linear systems. The purpose of this paper is to develop fast algorithms that cover this wider set of systems. An important feature of the general scheme introduced here is that it leads to the definition of two broad classes of matrices, called diagonal innovation matrices (DIM) and peripheral innovation matrices (PIM), for which fast schemes can be developed. The class of PIM matrices includes many structures appearing in signal processing applications. Most of them are extensively studied in this paper and Fortran coding is provided. Finally, ARMA modeling is considered and within the general framework already introduced, fast methods for the determination of the autoregressive (AR) portion of the ARMA model are presented.

A unifed view of parametric processing algorithms for prewindowed signals

Abstract This paper offers a unified overview of the algorithms developed for the processing of ‘prewindowed’ signals. The prewindowing assumption leads to simple and efficient schemes which find applications in many areas of modern DSP but especially in the digital communications field (adaptive equalization, echo cancellation, etc.). Algorithms for both least-squares filtering and linear prediction of multichannel signals are considered. The multichannel approach was chosen here instead of the single-channel one because in some situations the generalization of the single-channel case is not trivial. (The inverse is trivial.) On the other hand, an increasing number of researchers is willing to practice multichannel DSP (biological signals, beamforming techniques in radar applications, etc.) and can find in those algorithms a tool ‘ready for use’. The presentation covers fast order-recursive schemes and sequential methods for direct (transversal) and lattice-ladder implementations. In the latter case, normalized and unnormalized lattice-ladder forms are discussed. The derivation of all algorithms using a unified approach reveals the relationships among the various variables and between fast algorithms for direct and lattice-ladder structures.

Efficient recursive in order least squares FIR filtering and prediction

This paper is concerned with the efficient determination of the optimum, in the least squares sense, FIR filter on the basis of data samples of the input and desired response signals, by procedures recursive in the filter order. This situation typically arises when no a priori statistics are available and the system order is not known. The general multiinput-multioutput (multichannel) case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2S + 15m multiplications (mps) per order m, S being the number of samples. In the special case of linear prediction it calls for about S + 12m mps. Hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of Marple [1] and Morf et al. [2], respectively. Additionally, the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter.

Fast algorithms for block toeplitz matrices with toeplitz entries

Abstract This paper deals with efficient triangularization, inversion and system solution of block Toeplitz matrices with Toeplitz entries. Fast algorithms are developed which taking into advantage the joint Toeplitz structure, reduce by a factor of two the complexity of existing algorithms for general block Toeplitz matrices.

Word Length, Word Frequencies and Zipf’s Law in the Greek Language

The aim of this paper is to report for the first time the 1000 most common words and lemmas of Modern Greek and some of their quantitative characteristics. The frequency word list produced is based on the Hellenic National Corpus (HNC), a corpus of Modern Greek language consisting of about 13 million words of written texts. In particular, we investigate the application of Zipf’s law in both the 1000 most common words and lemmas. In addition we examine the frequency distribution of the grammatical categories in the 1000 most common words and lemmas as well as the average word length in the whole HNC and the growth of the average word length as a function of the number of the most common words.

QRS detection through time recursive prediction techniques

Abstract The purpose of this paper is to demonstrate the usefulness of time recursive prediction techniques for “event detection”. Both 3-lead and 1-lead ECG signals are used and QRS complexes are considered as events to be detected. Several detection criteria are tried and compared. A reference algorithm is employed on a standard ECG data base in order to evaluate the results obtained. A detection accuracy approximating 99% can be reported. Histograms presenting the relative position of detected QRSs to the reference value can be used both for validation of the method and to understand the behavior of recursive least squares algorithms on a specific signal.

SVD analysis by synthesis of harmonic signals

An analysis by synthesis procedure based on the singular value decomposition (SVD) methodology is proposed. Using this procedure, a criterion for detecting the number of sinusoidal signals in the presence of noise is defined. Consecutive reconstructions are performed, and the resulting error power is compared to the noise variance in order to get the best approximation of the original noncorrupted signal. The number of the singular values corresponding to a reconstruction error power as close as possible to the noise variance gives the parsimonious order. The existence of such a criterion is important for both high-quality reconstruction and spectral analysis. Various spectral estimation techniques used on a reconstructed signal make it possible to retrieve harmonics in a highly noisy environment with very short data lengths. >