M.O. Ahmad

Spatially Adaptive Wavelet-Based Method Using the Cauchy Prior for Denoising the SAR Images

The speckle noise complicates the human and automatic interpretation of synthetic aperture radar (SAR) images. Thus, the reduction of speckle is critical in various SAR image processing tasks. In this paper, we introduce a new spatially adaptive wavelet-based Bayesian method for despeckling the SAR images. The wavelet coefficients of the logarithmically transformed reflectance and speckle noise are modeled using the zero-location Cauchy and zero-mean Gaussian distributions, respectively. These prior distributions are then exploited to develop a Bayesian minimum mean absolute error estimator as well as a maximum a posteriori estimator. A new context-based technique with a reduced complexity is proposed for incorporating the spatial dependency of the wavelet coefficients with the Bayesian estimation processes. Experiments are carried out using typical noise-free images corrupted with simulated speckle noise as well as real SAR images, and the results show that the proposed method performs favorably in comparison to some of the existing methods in terms of the peak signal-to-noise ratio, speckle statistics and structural similarity index, and in its ability to suppress the speckle in the homogeneous regions

Video Denoising Based on Inter-frame Statistical Modeling of Wavelet Coefficients

The paper proposes a joint probability density function to model the video wavelet coefficients of any two neighboring frames and then applies this statistical model for denoising. The parameter of the density function that measures the correlation between the wavelet coefficients of the two frames is used as an index for the motion. The joint density function is employed for spatial filtering of the noisy wavelet coefficients by developing a bivariate maximum a posteriori estimator. A recursive time averaging of the spatially filtered wavelet coefficients is adopted for further noise reduction. Simulation results on test video sequences show an improved performance both in terms of the peak signal-to-noise ratio and the perceptual quality compared to that of the other denoising algorithms

Efficient Application of MUSIC Algorithm Under the Coexistence of Far-Field and Near-Field Sources

This correspondence is concerned with source localization and classification for scenarios where both the far-field and near-field narrowband sources may coexist. We propose an efficient MUSIC-based solution that requires neither a multidimensional search nor high-order statistics (HOS). We also derive the stochastic Cramér-Rao bound (CRB) for the problem under consideration. The performance of the proposed method is compared with an existing method and with the CRB.

Systolic algorithms and a memory-based design approach for a unified architecture for the computation of DCT/DST/IDCT/IDST

In this paper, an efficient design approach for a unified very large-scale integration (VLSI) implementation of the discrete cosine transform/discrete sine transform/inverse discrete cosine transform/inverse discrete sine transform based on an appropriate formulation of the four transforms into cyclic convolution structures is presented. This formulation allows an efficient memory-based systolic array implementation of the unified architecture using dual-port ROMs and appropriate hardware sharing methods. The performance of the unified design is compared to that of some of the existing ones. It is found that the proposed design provides a superior performance in terms of the hardware complexity, speed, I/O costs, in addition to such features as regularity, modularity, pipelining capability, and local connectivity, which make the unified structure well suited for VLSI implementation.

Results on maximally flat fractional-delay systems

The two classes of maximally flat finite-impulse response (FIR) and all-pass infinite-impulse response (IIR) fractional-sample delay systems are thoroughly studied. New expressions for the transfer functions are derived and mathematical properties revealed. Our contributions to the FIR case include a closed-form formula for the Farrow structure, a three-term recurrence relation based on the interpolation algorithm of Neville, a concise operator-based formula using the forward shift operator, and a continued fraction representation. Three types of structures are developed based on these formulas. Our formula for the Farrow structure enhances the existing contributions by Valimaki, and by Vesma and Sarama/spl uml/ki on the subsystems of the structure. For the IIR case, it is rigorously proved, using the theory of Pade approximants, that the continued fraction formulation of Tassart and Depalle yields all-pass fractional delay systems. It is also proved that the maximally flat all-pass fractional-delay systems are closely related to the Lagrange interpolation. It is shown that these IIR systems can be characterized using Thieles rational interpolation algorithm. A new formula for the transfer function is derived based on the Thiele continued fractions. Finally, a new class of maximally flat FIR fractional-sample delay systems that exhibit an almost all-pass magnitude response is proposed. The systems possess a maximally flat group-delay response at the end frequencies 0 and /spl pi/, and are characterized by a closed-form formula. Their main advantage over the classical FIR Lagrange interpolators is the improved magnitude response characteristics.

A New Statistical Detector for DWT-Based Additive Image Watermarking Using the Gauss–Hermite Expansion

Traditional statistical detectors of the discrete wavelet transform (DWT)-based image watermarking use probability density functions (PDFs) that show inadequate matching with the empirical PDF of image coefficients in view o f the fact that they use a fixed number of parameters. Hence, the decision values obtained from the estimated thresholds of these detectors provide substandard detection performance. In this paper, a new detector is proposed for the DWT-based additive image watermarking, wherein a PDF based on the Gauss-Hermite expansion is used, in view of the fact that this PDF provides a better statistical match to the empirical PDF by utilizing an appropriate number of parameters estimated from higher-order moments of the image coefficients. The decision threshold and the receiver operating characteristics are derived for the proposed detector. Experimental results on test images demonstrate that the proposed watermark detector performs better than other standard detectors such as the Gaussian and generalized Gaussian (GG), in terms of the probabilities of detection and false alarm as well as the efficacy. It is also shown that detection performance of the proposed detector is more robust than the competitive GG detector in the case of compression, additive white Gaussian noise, filtering, or geometric attack.

Bayesian Wavelet-Based Image Denoising Using the Gauss–Hermite Expansion

The probability density functions (PDFs) of the wavelet coefficients play a key role in many wavelet-based image processing algorithms, such as denoising. The conventional PDFs usually have a limited number of parameters that are calculated from the first few moments only. Consequently, such PDFs cannot be made to fit very well with the empirical PDF of the wavelet coefficients of an image. As a result, the shrinkage function utilizing any of these density functions provides a substandard denoising performance. In order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments, a PDF using a series expansion in terms of the Hermite polynomials that are orthogonal with respect to the standard Gaussian weight function, is introduced. A modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients, ensuring at the same time the resulting PDF to be non-negative. It is shown that the proposed PDF matches the empirical one better than some of the standard ones, such as the generalized Gaussian or Bessel K-form PDF. A Bayesian image denoising technique is then proposed, wherein the new PDF is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients. Experimental results on several test images demonstrate that the proposed denoising method, both in the subband-adaptive and locally adaptive conditions, provides a performance better than that of most of the methods that use PDFs with limited number of parameters.

A new radix-2/8 FFT algorithm for length-q/spl times/2/sup m/ DFTs

In this paper, a new radix-2/8 fast Fourier transform (FFT) algorithm is proposed for computing the discrete Fourier transform of an arbitrary length N=q/spl times/2/sup m/, where q is an odd integer. It reduces substantially the operations such as data transfer, address generation, and twiddle factor evaluation or access to the lookup table, which contribute significantly to the execution time of FFT algorithms. It is shown that the arithmetic complexity (multiplications+additions) of the proposed algorithm is, in most cases, the same as that of the existing split-radix FFT algorithm. The basic idea behind the proposed algorithm is the use of a mixture of radix-2 and radix-8 index maps. The algorithm is expressed in a simple matrix form, thereby facilitating an easy implementation of the algorithm, and allowing for an extension to the multidimensional case. For the structural complexity, the important properties of the Cooley-Tukey approach such as the use of the butterfly scheme and in-place computation are preserved by the proposed algorithm.

A systolic array architecture for the discrete sine transform

An efficient approach to design very large scale integration (VLSI) architectures and a scheme for the implementation of the discrete sine transform (DST), based on an appropriate decomposition method that uses circular correlations, is presented. The proposed design uses an efficient restructuring of the computation of the DST into two circular correlations, having similar structures and only one half of the length of the original transform; these can be concurrently computed and mapped onto the same systolic array. Significant improvement in the computational speed can be obtained at a reduced input-output (I/O) cost and low hardware complexity, retaining all the other benefits of the VLSI implementations of the discrete transforms, which use circular correlation or cyclic convolution structures. These features are demonstrated by comparing the proposed design with some of the previously reported schemes.

A closed-form solution to the least-square design problem of 2-D linear-phase FIR filters

In this paper, the least-square design problem of a general two-dimensional (2-D) linear-phase FIR filter with an arbitrary magnitude response is studied. By minimizing the frequency-domain error function and exploiting some of the properties of the functions and matrices associated with the design problem, a novel closed-form solution is developed. The solution is expressed in terms of the desired magnitude specifications and is eventually presented as an explicit expression for the impulse response of the filter to be designed, making a very fast evaluation of the filters coefficients possible. It is also shown that when this solution is used to design filters that have centrosymmetric and quadrantally symmetric magnitude responses, some further computational savings can be achieved. Several design examples illustrating the effectiveness of the proposed solution are considered.