Showing papers by "M. Omair Ahmad published in 2009"

A fast 8×8 transform for image compression

Abstract: In this paper, we propose an efficient 8×8 transform matrix for image compression by appropriately introducing some zeros in the 8×8 signed DCT matrix. We show that the proposed transform is orthogonal, which is a highly desirable property. In order to make this novel transform more attractive for recent real-time applications, we develop an efficient algorithm for its fast computation. By using this algorithm, the proposed transform requires only 18 additions to transform an 8-point sequence. Compared to the existing 8×8 approximated DCT matrices, it is shown that savings of 25% in the number of arithmetic operations can easily be achieved using the proposed transform operator without noticeable degradations in the reconstructed images. We also present simulation results using some standard test images to show the efficiency of the proposed transform in image compression.

Orthogonalized discriminant analysis based on generalized singular value decomposition

Abstract: Generalized singular value decomposition (GSVD) has been used for linear discriminant analysis (LDA) to solve the small sample size problem in pattern recognition. However, this algorithm may suffer from the over-fitting problem. In this paper, we propose a novel orthogonalization technique for the LDA/GSVD algorithm to address the over-fitting problem. In this technique, an orthogonalization of the basis of the discriminant subspace derived from the LDA/GSVD algorithm is carried out through an eigen-decomposition of a small size inner product matrix. It is computationally efficient when data are high dimensional. The technique is further applied to the kernelized LDA/GSVD algorithm, mGSVD-KDA, leading to a new algorithm, referred to as GSVD-OKDA. It is shown that with linear and nonlinear kernels, this new algorithm successfully overcomes the over-fitting problem of the LDA/GSVD and mGSVD-KDA algorithms. Simulation results show that the proposed algorithms provide high recognition accuracy with low computational complexity.

Orthogonalized linear discriminant analysis based on modified generalized singular value decomposition

Abstract: Generalized singular value decomposition (GSVD) has been used in the literature for linear discriminant analysis (LDA) to solve the small sample size problem in pattern recognition. However, this algorithm suffers from excessive computational load when the sample dimension is high. In this paper, we present a modified version of the LDA/GSVD algorithm to enhance the computational efficiency, referred to as EGSVD-LDA algorithm, which uses the linear combination of the sample vectors to represent the singular vectors so as to circumvent the calculation of the high dimensional singular vectors through SVD. Further, to overcome the over-fitting problem of the GSVD-based algorithms, we have also proposed a new method to orthogonalize the discriminative subspace derived from the GSVD framework through a Gram-Schmidt process in an inner product space. These methods are efficient when data are high dimensional. Simulation results show that the EGSVD-LDA algorithm, especially its orthogonalized version, overcomes the computational complexity problem and provides high recognition accuracy with low computational load.

A new bivariate MAP estimator for DT-CWT-based video denoising

Abstract: A new bivariate maximum a posteriori estimator is proposed for the magnitude components of the dual-tree complex wavelet transform (DT-CWT) coefficients in order to reduce additive white Gaussian noise in a video. The estimator considers the fact that the magnitude components of the DT-CWT coefficients of the Gaussian distributed noise fit the generalized Gamma distribution very well [1]. For spatial filtering, the joint distribution function of the magnitude components of the DT-CWT coefficients of the two neighboring frames of a video is considered to be locally-adaptive bivariate Gaussian having a non-negative mean. The correlation coefficient of this distribution function acts as an indirect measure of the motion of the DT-CWT coefficients between two neighboring frames. A recursive time averaging of the spatially filtered magnitude components is adopted for further noise reduction. Experimental results on test video sequences show that the proposed estimator provides an average peak signal-to-noise ratio that is higher than that provided by the others.

A residual-cepstrum method of pitch estimation from noisy speech

Abstract: Residual and cepstral representations of speech were utilized to estimate pitch in a noisy environment. It was found that the major excitation of the vocal tract within a pitch period occurred at the instant of glottal closure (GC). It was possible to determine the pitch period by careful analysis of the speech signal with the help of GC instants. A discrete Fourier transform (DFT) based power cepstrum (DFTPC) was proposed to overcome the adverse effect of noise on the Hilbert envelope (HE) and residual signal (RS). The DFTPC of the HE exhibited a more prominent pitch-peak in a heavily degraded condition in comparison to that demonstrated by the conventional cepstrum of the noisy speech. Simulation results indicated that the global maximization of the DFTPC yielded an accurate pitch estimate as compared to the latest models for a wide range of speakers in noisy environments.