Hon Keung Kwan

A fuzzy neural network and its application to pattern recognition

Defines four types of fuzzy neurons and proposes the structure of a four-layer feedforward fuzzy neural network (FNN) and its associated learning algorithm. The proposed four-layer FNN performs well when used to recognize shifted and distorted training patterns. When an input pattern is provided, the network first fuzzifies this pattern and then computes the similarities of this pattern to all of the learned patterns. The network then reaches a conclusion by selecting the learned pattern with the highest similarity and gives a nonfuzzy output. The 26 English alphabets and the 10 Arabic numerals, each represented by 16/spl times/16 pixels, were used as original training patterns. In the simulation experiments, the original 36 exemplar patterns were shifted in eight directions by 1 pixel (6.25% to 8.84%) and 2 pixels (12.5% to 17.68%). After the FNN has been trained by the 36 exemplar patterns, the FNN can recall all of the learned patterns with 100% recognition rate. It can also recognize patterns shifted by 1 pixel in eight directions with 100% recognition rate and patterns shifted by 2 pixels in eight directions with an average recognition rate of 92.01%. After the FNN has been trained by the 36 exemplar patterns and 72 shifted patterns, it can recognize patterns shifted by 1 pixel with 100% recognition rate and patterns shifted by 2 pixels with an average recognition rate of 98.61%. The authors have also tested the FNN with 10 kinds of distorted patterns for each of the 36 exemplars. The FNN can recognize all of the distorted patterns with 100% recognition rate. The proposed FNN can also be adapted for applications in some other pattern recognition problems. >

A neural network approach to pulse radar detection

A multilayer feedforward neural network is applied to pulse compression. The 13-element Barker code and the maximum-length sequences (m-sequences) with lengths 15, 31, and 63 b were used as the signal codes, and four networks were implemented, respectively. In each of these networks, the number of input units was the same as the signal length while the number of hidden units was three and the number of output units was one. In training each of these networks, backpropagation learning was used and the number of training epochs was 500. Using this approach, a more than 40 dB output peak signal-to-sidelobe ratio can be achieved. These fault-tolerant neural networks can provide a robust means for pulse radar detection. >

IIR Digital Filter Design With New Stability Constraint Based on Argument Principle

This paper presents a weighted least squares (WLS) method for IIR digital filter design using a new stability constraint. Utilizing the reweighting technique, an iterative second-order cone programming (SOCP) method is employed to solve the design problem, such that either linear or second-order cone constraints can be further incorporated. In order to guarantee the stability of designed IIR digital filters, a new stability constraint with a prescribed pole radius is derived from the argument principle (AP) of complex analysis. As compared with other frequency-domain stability constraints, the AP-based stability constraint is both sufficient and necessary. Since the derived stability constraint cannot be directly incorporated in the iterative SOCP method, the similar reweighting technique is deployed to approximate the stability constraint in a quadratic form, which is then combined with the WLS iterative design process. Filter design examples are presented to demonstrate the effectiveness of the proposed iterative SOCP method.

Multilayer feedforward neural networks with single powers-of-two weights

A new algorithm for designing multilayer feedforward neural networks with single powers-of-two weights is presented. By applying this algorithm, the digital hardware implementation of such networks becomes easier as a result of the elimination of multipliers. This proposed algorithm consists of two stages. First, the network is trained by using the standard backpropagation algorithm. Weights are then quantized to single powers-of-two values, and weights and slopes of activation functions are adjusted adaptively to reduce the sum of squared output errors to a specified level. Simulation results indicate that the multilayer feedforward neural networks with single powers-of-two weights obtained using the proposed algorithm have generalization performance similar to that of the original networks with continuous weights. >

Minimax Design of IIR Digital Filters Using SDP Relaxation Technique

This paper presents a new algorithm using semidefinite programming (SDP) relaxation to design infinite impulse response digital filters in the minimax sense. Unlike traditional design algorithms that try to directly minimize the error limit, the proposed algorithm employs a bisection searching procedure to locate the minimum error limit of the approximation error. Given a fixed error limit at each iteration, the SDP relaxation technique is adopted to formulate the design problem in a convex form. In practice, the true minimax design cannot be always obtained. Thus, a regularized feasibility problem is adopted in the bisection searching procedure. The stability of the designed filters can also be guaranteed by adjusting the regularization coefficient. Unlike other sequential design methods, the proposed algorithm tries to find a feasible solution at each iteration of the sequential design procedure within a feasible set defined by the relaxed constraints. This feasible set is not restricted within the neighborhood of a given point obtained from the previous iteration. Thus, the proposed method can avoid being trapped in the locally minimum point. Four examples are presented in this paper to demonstrate the effectiveness of the proposed method.

Peak-Error-Constrained Sparse FIR Filter Design Using Iterative SOCP

In this paper, a novel algorithm is proposed to design sparse FIR filters. It is known that this design problem is highly nonconvex due to the existence of -norm of a filter coefficient vector in its objective function. To tackle this difficulty, an iterative procedure is developed to search a potential sparsity pattern, which is then used to compute the final solution by solving a convex optimization problem. In each iterative step, the original sparse filter design problem is successively transformed to a simpler subproblem. It can be proved that under a weak condition, globally optimal solutions of these subproblems can be attained by solving their dual problems. In this case, the overall iterative procedure converges to a locally optimal solution of the original design problem. The design procedure described above can be repeated for several times to further improve the sparsity of design results. The output of the previous stage can be used as the initial point of the subsequent design. The performance of the proposed algorithm is evaluated by two sets of design examples, and compared to other sparse FIR filter design algorithms.

Numerical representation of DNA sequences

DNA sequence analysis using digital signal processing requires conversion of a base sequence to a numerical sequence. The choice of the numerical representation of a DNA sequence affects how well its biological properties can be reflected in the numerical domain for the detection and identification of the characteristics of special regions of interest. This paper presents some selected methods of DNA numerical representation for DNA sequence analysis, discusses their relative merits and demerits, and includes some concluding remarks.

Fuzzy Filters for Noise Reduction in Images

In this chapter, seven fuzzy filters for noise reduction in images are introduced. These seven fuzzy filters include the Gaussian fuzzy filter with median center (GMED), the symmetrical triangular fuzzy filter with median center (TMED), the asymmetrical triangular fuzzy filter with median center (ATMED), the Gaussian fuzzy filter with moving average center (GMAV), the symmetrical triangular fuzzy filter with moving average center (TMAV), the asymmetrical triangular fuzzy filter with moving average center (ATMAV), and the decreasing weight fuzzy filter with moving average center (DWMAV). Each of these fuzzy filters, applies a weighted membership function to an image within a window to determine the center pixel, is easy and fast to implement. Simulation results on the filtering performance of these seven fuzzy filters and the standard median filter (MED) and moving average filter (MAV) on images contaminated with low, medium, high impulse and random noises are presented. Results indicate that these seven fuzzy filters achieve varying successes in noise reduction in images as compared to the standard MED and MAV filters.

Fuzzy filters for image filtering

In this paper, four fuzzy filters for filtering images contaminated with random, impulse, and sum of random and impulse noises are introduced. In each of these four fuzzy filters, the output pixel of a filtered image at the center of a moving window area is defined as a normalized sum of weighted input pixels within the window. Simulation results indicate that some of these fuzzy filters show improvement over the standard median and moving average filters in reducing these three noises.

FIR, Allpass, and IIR Variable Fractional Delay Digital Filter Design

This paper presents two-step design methodologies and performance analyses of finite-impulse response (FIR), allpass, and infinite-impulse response (IIR) variable fractional delay (VFD) digital filters. In the first step, a set of fractional delay (FD) filters are designed. In the second step, these FD filter coefficients are approximated by polynomial functions of FD. The FIR FD filter design problem is formulated in the peak-constrained weighted least-squares (PCWLS) sense and solved by the projected least-squares (PLS) algorithm. For the allpass and IIR FD filters, the design problem is nonconvex and a global solution is difficult to obtain. The allpass FD filters are directly designed as a linearly constrained quadratic programming problem and solved using the PLS algorithm. For IIR FD filters, the fixed denominator is obtained by model reduction of a time-domain average FIR filter. The remaining numerators of the IIR FD filters are designed by solving linear equations derived from the orthogonality principle. Analyses on the relative performances indicate that the IIR VFD filter with a low-order fixed denominator offers a combination of the following desirable properties including small number of denominator coefficients, lowest group delay, easily achievable stable design, avoidance of transients due to nonvariable denominator coefficients, and good overall magnitude and group delay performances especially for high passband cutoff frequency ( ges 0.9pi) . Filter examples covering three adjacent ranges of wideband cutoff frequencies [0.95, 0.925, 0.9], [0.875, 0.85, 0.825], and [0.8, 0.775, 0.75] are given to illustrate the design methodologies and the relative performances of the proposed methods.