In this paper, a new similarity measure for fractal image compression (FIC) is introduced. In the proposed Huber fractal image compression (HFIC), the linear Huber regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression. When the original image is corrupted by noises, we argue that the fractal image compression scheme should be insensitive to those noises presented in the corrupted image. This leads to a new concept of robust fractal image compression. The proposed HFIC is one of our attempts toward the design of robust fractal image compression. The main disadvantage of HFIC is the high computational cost. To overcome this drawback, particle swarm optimization (PSO) technique is utilized to reduce the searching time. Simulation results show that the proposed HFIC is robust against outliers in the image. Also, the PSO method can effectively reduce the encoding time while retaining the quality of the retrieved image.

As is well known in statistics, the resulting linear regressors by using the rank-based Wilcoxon approach to linear regression problems are usually robust against (or insensitive to) outliers. This motivates us to introduce in this paper the Wilcoxon approach to the area of machine learning. Specifically, we investigate four new learning machines, namely Wilcoxon neural network (WNN), Wilcoxon generalized radial basis function network (WGRBFN), Wilcoxon fuzzy neural network (WFNN), and kernel-based Wilcoxon regressor (KWR). These provide alternative learning machines when faced with general nonlinear learning problems. Simple weights updating rules based on gradient descent will be derived. Some numerical examples will be provided to compare the robustness against outliers for various learning machines. Simulation results show that the Wilcoxon learning machines proposed in this paper have good robustness against outliers. We firmly believe that the Wilcoxon approach will provide a promising methodology for many machine learning problems.

Fractal image compression exploits the self-similarity of an image to achieve image compression. The conventional algorithm allows the transformations on domain blocks to obtain eight orientations so as to increase the quality of retrieved image. On the other hand, if no transformation is performed in order to speedup the encoder, the image quality will decay. In this paper, a direct allocating method to predict the desired transformation for similarity measure is proposed. Simulations show that the encoding time is almost the same as that of the method without transformations while the image quality is close to that of the standard method.

The well-known (two-parameter) sequential minimal optimization (2PSMO) algorithm for support vector classification is generalized to three-parameter sequential minimal optimization (3PSMO) algorithm in this paper. This new algorithm retains all the good properties of the former one. The main difference between these two algorithms is that the optimization is performed in each iteration of the 2PSMO algorithm on a line segment, whilst that of the 3PSMO algorithm on a region consisting of infinitely many line segments. Four public data sets are used to show the performance of both algorithms.

In this paper, the Particle Swarm Optimization (PSO) is utilized to enhance the concavity searching for the control points of Active Contour Model (ACM). In the traditional methods for ACM, the best candidates are searched in a small window. Consequently, the boundary concavities cannot be searched accurately. Some improvements have been made in the past to enlarge the searching space, yet they are still time-consuming. To overcome these drawbacks, a multi-population particle swarm optimization technique is adopted in this paper to reduce the search time but in a larger searching window. This optimizer inherits the spirit of the original PSO as well as shares information among the swarms surrounding control points. Experimental results demonstrate that the proposed method can improve the search of object concavities without spending extra time.

In this paper, a high efficient decoding algorithm is developed here in order to correct both erasures and errors for Reed-Solomon (RS) codes based on the Euclidean algorithm together with the Berlekamp-Massey (BM) algorithm. The new decoding algorithm computes the errata locator polynomial and the errata evaluator polynomial simultaneously without performing polynomial divisions, and there is no need for the computation of the discrepancies and the field element inversions. Also, the separate computation of the Forney syndrome needed in the decoder is completely avoided. As a consequence, the complexity of this new decoding algorithm is dramatically reduced. Finally, the new algorithm has been verified through a software simulation using C/sup ++/ language. An illustrative example of (255,239) RS code using this program shows that the speed of the decoding process is approximately three times faster than that of the inverse-free Berlekamp-Massey algorithm.

The central problem in the implementation of a Reed-Solomon code is finding the roots of the error locator polynomial. In 1967, Berlekamp et al. found an algorithm for finding the roots of an affine polynomial in GF(2/sup m/) that can be used to solve this problem. In this paper, it is shown that this Berlekamp-Rumsey-Solomon (1967) algorithm, together with the Chien (1964) search method, makes possible a fast decoding algorithm in the standard-basis representation that is naturally suitable in a software implementation. Finally, simulation results for this fast algorithm are given.

In this paper, a fast encoding algorithm is developed for fractal image compression. At each search entry in the domain pool, the mean square error (MSE) calculations of the given range block and the eight dihedral symmetries of the domain block are obtained simultaneously in the frequency domain, in which the redundant computations are all eliminated in the new encoding algorithm. It is shown in software simulation that the encoding time is about six times faster than that of the baseline method with almost the same PSNR for the retrieved image. The fast algorithm is performed to deal with the eight dihedral symmetries at each search entry. Therefore, it can be applied to various enhanced algorithms which are equipped with quadtree, classification, and other mechanisms.

This paper presents a fast algorithm to perform the 2-D discrete periodized wavelet transform based on the operator correlation algorithm (OCA). The OCA-based algorithm needs half of the multiplications and bits required by the classical algorithm. The OCA-based algorithm is modular inherent. It can be easily mapped to VLSI design.

In a previous article by Truong et al. (see ibid., vol.46, p.973-76, 1998), it was shown that an inverse-free Berlekamp-Massey (1968, 1969) algorithm can be generalized to find the error locator polynomial in a Reed-Solomon (RS) decoder for correcting errors as well as erasures. The basic idea of this procedure is the replacement of the initial condition of an inverse-free BM algorithm by the Forney (1965) syndromes. It is shown that the errata locator polynomial can be obtained directly by initializing an inverse-free BM algorithm with the erasure locator polynomial and the syndromes. An important ingredient of this new algorithm is a modified BM algorithm for computing the errata locator polynomial. As a consequence, the separate computation of the erasure locator polynomial and the Forney syndrome, needed in the decoder developed by Truong et al., are completely avoided in this modification of the BM algorithm. This modified algorithm requires fewer finite field addition and multiplication operations than the previous algorithm. Finally, the new decoding method was implemented on a computer using C++ language. It is shown in a simulation that the speed of this new decoder is faster than the decoder developed by Truong et al. An example using this program is given for an (255, 239) RS code for correcting errors and erasures with 2/spl nu/+s/spl les/10.

Previously, the authors proposed an inverse-free Berlekamp-Massey (1968, 1969) algorithm to simplify the Reed-Solomon (RS) codes. This modified RS decoding method is the best known technique for finding the error locator polynomial. The inverse-free method is generalized to find both errors and erasures. The basic idea of the new procedure is the replacement of the initial condition of the BM algorithm by the Forney (1965) syndromes. With this improved technique, the complexity of time-domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches.