Kah-Chye Tan

Probabilistic neural-network structure determination for pattern classification

Network structure determination is an important issue in pattern classification based on a probabilistic neural network. In this study, a supervised network structure determination algorithm is proposed. The proposed algorithm consists of two parts and runs in an iterative way. The first part identifies an appropriate smoothing parameter using a genetic algorithm, while the second part determines suitable pattern layer neurons using a forward regression orthogonal algorithm. The proposed algorithm is capable of offering a fairly small network structure with satisfactory classification accuracy.

Postprocessing method for suppressing musical noise generated by spectral subtraction

We investigate whether musical noise, which often exists in speech enhanced using spectral subtraction, can be suppressed. Via exploiting some specific characteristics of human speech, we propose a method that can effectively suppress musical noise without a noticeable effect on speech intelligibility. Performance assessments confirm that our method is effective.

Kalman-filtering speech enhancement method based on a voiced-unvoiced speech model

In this work, we are concerned with optimal estimation of clean speech from its noisy version based on a speech model we propose. We first propose a (single) speech model which satisfactorily describes voiced and unvoiced speech and silence (i.e., pauses between speech utterances), and also allows for exploitation of the long term characteristics of noise. We then reformulate the model equations so as to facilitate subsequent application of the well-established Kalman filter for computing the optimal estimate of the clean speech in the minimum-mean-square-error sense. Since the standard algorithm for Kalman-filtering involves multiplications of very large matrices and thus demands high computational cost, we devise a mathematically equivalent algorithm which is computationally much more efficient, by exploiting the sparsity of the matrices concerned. Next, we present the methods we use for estimating the model parameters and give a complete description of the enhancement process. Performance assessment based on spectrogram plots, objective measures and informal subjective listening tests all indicate that our method gives consistently good results. As far as signal-to-noise ratio is concerned, the improvements over existing methods can be as high as 4 dB.

Linear independence of steering vectors of an electromagnetic vector sensor

We investigate linear independence of steering vectors of one electromagnetic vector sensor. We show that every three steering vectors with distinct directions of arrival (DOAs) are linearly independent. We also show that four steering vectors with distinct DOAs are linearly independent if the ellipticity angles of the signals associated with any two of the four steering vectors are distinct. Moreover, every four steering vectors corresponding to circularly polarized signals with the same spin direction are linearly dependent. We then establish that five steering vectors are linearly independent if exactly two or three of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any five steering vectors, then for any DOA there exists a steering vector that is linearly dependent on the five steering vectors.

Estimating directions of arrival of completely and incompletely polarized signals with electromagnetic vector sensors

We are concerned with direction-of-arrival estimation and signal classification with electromagnetic vector sensors for scenarios where completely and incompletely polarized signals may co-exist. We propose an efficient ESPRIT-based method, address the identifiability of the proposed method, and compare its performance against CRB.

Efficient method for estimating directions-of-arrival of partially polarized signals with electromagnetic vector sensors

We have developed a high-resolution ESPRIT-based method for estimating the directions-of-arrival of partially polarized signals with electromagnetic vector sensors, each of which provides measurements of the complete electric and magnetic fields induced by electromagnetic signals. The method is computationally efficient since unlike many high-resolution methods, it does not involve searching across a multidimensional array manifold. In addition, the method has two variants, of which one is applicable to scenarios where a priori information about the array system, such as the sensor positions, is unavailable.

An investigation on number of signals whose directions-of-arrival are uniquely determinable with an electromagnetic vector sensor

Abstract We first study a theorem on the relationship among linear dependence of steering vectors, correlation among signals, and the number of signals whose DOAs are uniquely determinable, which was derived by Wax and Ziskind (1989) and Nehorai et al. (1991) for a class of scalar-sensor arrays. We then extend the theorem to include all scalar-sensor arrays, as well as vector-sensor arrays receiving polarized signals. We further generalize the first part of the theorem to include vector-sensor arrays receiving general signals (which can be polarized, partially polarized or unpolarized). Subsequently, we show that the DOAs of two uncorrelated signals can be uniquely determined with one electromagnetic vector sensor, regardless of the states of polarization. However, it may be impossible to determine uniquely the DOAs of two fully correlated signals. Finally, we establish a relationship between uniqueness in measurements and uniqueness in MUSIC estimates.

Linear dependence of steering vectors associated with tripole arrays

We are concerned with the linear independence of steering vectors associated with tripoles, each of which provides measurements of the three components of electric field induced by electromagnetic signals. We first establish that for a single tripole, any steering vector is linearly dependent on at least one other steering vector corresponding to a different direction-of-arrival (DOA) for a general problem where signals may arrive from anywhere in a three-dimensional (3-D) space, but every two steering vectors with distinct DOAs are linearly independent if the signals are nonlinearly polarized and arrive from a strictly hemispherical space. We then obtain a series of upper bounds for the number of linearly independent steering vectors associated with a tripole array with general sensor configurations. We also show that for applications where signals are known to be linearly polarized in the same direction, the ability to estimate DOAs using a tripole array is identical to that using a scalar-sensor array if both of them have identical sensor configurations.

Restoration of real-world motion-blurred images

Abstract Estimating the PSF of a real-world motion-blurred image is an essential step in the restoration process. To estimate the PSF, some techniques assume that it is a spatially invariant square pulse, and extract the blur extent from the zero-crossings of the averaged power spectrum. Some techniques make use of special features such as isolated point objects or sharp edges in a homogeneous background. Recently, sophisticated methods based on maximum likelihood estimators have been developed for estimation of symmetrical PSFs. In actual applications, we often encountered motion-blurred images which have asymmetrical PSFs. There are also no special features such as isolated points. These images present challenges which are not satisfactorily met by the above techniques. In this paper, we first study the error characteristics due to the use of inappropriate PSFs. On the basis of the results, we develop a procedure for estimating (possibly) asymmetrical PSFs of real-world motion-blurred images. The procedure starts with a preliminary restoration using a ramp PSF. The result will indicate if a ramp PSF, a square pulse PSF, or a trapezoid PSF is appropriate, and also provide an estimate for the blur extent of the appropriate PSF. Images restored according to the procedure are practically free of ghost or ringing patterns. The effectiveness and practicality of the proposed procedure is tested using a few real-world images blurred with unknown PSF.

Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment

Abstract The sensitivity of the inverse filter to noise is often thought to be the reason that inverse filter restorations of motion-blurred images are normally dominated by errors. In this paper, we show that even in the absence of noise, there is a large error component, called the edge error, that arises due to the fact that real images seldom have the periodicity implicitly assumed by discrete Fourier transform operation. An analysis shows that the edge error has a triangular-wave structure with an amplitude proportional to the difference between the average pixel intensity levels of the left and right edges of the image. For the central region of an image, the edge error may be reduced by using Wiener filtering instead of inverse filtering. However, the restored images show reduced resolution as well as ghosting and ringing effects. We also derive mathematically a special window for treatment of the edge error. A significant improvement in the quality of restorations is achieved with the use of this special window. The best restorations are obtained by subjecting the windowed-blurred image to a Wiener filter of large signal-to-noise ratio.