This paper analyzes the steady-state properties of a CORDIC-based adaptive ARMA lattice filter. In our previous study, the convergence properties of the filter in the non-steady state were clarified; however, its behavior in the steady state was not discussed. Therefore, we develop a distinct analysis technique based on a Markov chain in order to investigate the steady-state properties of the filter. By using the proposed technique, the relationship between step size and coefficient estimation error is revealed.

In the field of the restoration of motion blurred images, several deterministic techniques are proposed. Motion blurred images, however, include an ambiguity intrinsically. Therefore, the statistical restoration techniques are suited for the aim. In this paper, we describe the statistical properties of images blurred by various motions in mean square error sense since the discussions on the subject have been not presented in the past. The mean square errors of images blurred by motions and of images restored by Wiener filtering are formulated. The relations between the mean square errors and the extent of the motion blur or the correlation coefficient of the object are presented. The differences of the mean square errors among the various motions are discussed. Furthermore, these formulations are expanded to the motion blurred images imbedded by additive noise.

In this paper, the relationship between the recursive least square (RLS) method with a U-D decomposition algorithm and ARMA lattice filter realization algorithm is presented. Both the RLS method and the lattice filter realization algorithm are used for the same applications, such as model identification, etc., therefore, it is expected that the lattice filter algorithm is in some ways related to the RLS. Though some of the proposed lattice filter algorithms have been derived by the RLS method, they do not express the relationship between RLS snd ARMA lattice filter realization algorithm. In order to describe the relation clearly, a new structure of ARMA lattice filter is proposed. Further, based on the relationship, a method of model identification with frequency weighting (MIFW), which is different from a previous method, is derived. The new MIFW method modifies the lattice parameters which are acquired without a frequency weighting and obtain the parameters of an ARMA model, which is identified with frequency weighting. The proposed MIFW method has the following restrictions: (1) The used frequency weighting is FIR filter with a low order. (2) By using the parameters of the ARMA lattice filter with ARMA (N,M) order and the frequency weighting with L order, the new ARMA parameter with the frequency weignting is with ARMA(N-L,M-L) order. By using the proposed MIFW method, the ARMA parameters estimated with the frequency weighting can be obtained without starting the computation again.

This paper proposes a method to transform a CORDIC ARMA lattice filter, which is originally realized for signal analysis, into a signal synthesis lattice filter (CORDIC ARMA lattice synthesis filter). In order to perform such a transformation and then obtain the CORDIC ARMA lattice synthesis filter, we must implement the followings with CORDIC: (1) the structure of the altered lattice filter; and (2) an angle calculation module. However, we cannot achieve such an implementation as an extension of the CORDIC ARMA lattice filter algorithm. Therefore, this paper proposes CORDIC implementation schemes for both the structure and module, and then we realize the CORDIC ARMA lattice synthesis filter. By using CORDIC processors, the elementary sections of the CORDIC ARMA lattice synthesis filter are efficiently implemented without any multipliers. Since the obtained signal synthesis lattice filter consists of dedicated CORDIC processors, it keeps the advantage of the CORDIC ARMA lattice filter, that is a simple structure.

This paper proposes an Iterated Function System (IFS) which can reduce effects of quantization errors of the IFS parameters. The proposed method skips conventional analog-parameter search and directly selects optimum IFS parameters from pools of discrete IFS parameters. In conventional IFS-based image coding the IFS parameters are quantized after their analog optimum values are determined. The image reconstructed from the quantized parameters is degraded with errors that are traced back to quantization errors amplified in the iterated mappings. The effectiveness of this new realistic approach is demonstrated by simulation results over the conventional method.

This letter presents a significant property of the mapping parameters that play a central role to represent a given signal in Fractal Interpolation Functions (FIF). Thanks to our theoretical analysis, it is derived that the mapping parameters required to represent a given signal are also applicable to represent the upsampled signal of a given one. Furthermore, the upsampled signal obtained by using the property represents the self-affine property more distinctly than the given signal. Experiments show the validity and usefulness of the significant property.

In this paper, quantization method which can keep the phase and gain characteristics of a reference filter is proposed. The proposed method uses a genetic algorithm and a simulated annealing algorithm. The objective function used in this method is described with two kinds of weighting functions for identifying the phase and gain characteristics respectively. Therefore, the quantization accuracy on the gain characteristic is independent of the accuracy on the phase characteristic. Further, the proposed algorithm can be applied to any types of filters, because the chromosome expresses only their coefficients values. The efficiency of the proposed algorithm is verified by some experiments.

In this paper, a novel description method of the contour of a shape using extended fractal interpolation functions (EFIFs) is presented. Although the scope of application of traditional FIFs has been limited to cases in which a given signal is represented by a single-valued function, the EFIFs derived by the introduction of a new parameter can describe a multiple-valued signal such as the contour of a shape with a high level of accuracy. Furthermore, the proposed description method possesses the useful property that once a given contour has been modeled by the proposed description method, the shape can be easily expanded at an arbitrary expansion rate. Experimental results show the effectiveness and usefulness of the proposed description method for representing contours.

This letter proposes a method to transform normalized ARMA lattice filters, which are originally realized for signal analysis, into signal synthesis lattice filters. Although the transformation method has been proposed for normalized ARMA lattice filters with the MA order which is greater than or equal to the AR order, it has not been done when the AR order is greater than the MA order. With the proposed method, once an ARMA lattice filter with the AR order greater than the MA order is realized, then it can be transformed to the signal synthesis filter.

This paper presents a new fast and robust circle extraction method that is capable of extracting circles from images with complicated backgrounds. It is not based on the Hough transform (HT) that requires a time-consuming voting process. The proposed method uses a least-squares circle fitting algorithm for extracting circles. The arcs are fitted by extended digital lines that are extracted by a fast line extraction method. The proposed method calculates accurate circle parameters using the fitted arcs instead of evidence histograms in the parameter space. Tests performed on various real-world images show that the proposed method quickly and accurately extracts circles from complicated and heavily corrupted images.

This paper presents a cost-effective CORDIC-based architecture for adaptive lattice filters. An implementation method for an ARMA lattice filter using the CORDIC algorithm has been proposed. The previously proposed method can provide a simple filter architecture; however, it has problems such as redundant structure and numerical inaccuracy. Therefore, by solving each problem we derive a new non-redundant filter architecture with improved numerical accuracy. The obtained filter architecture provides a low cost ARMA lattice filter in which high-precision data processing is feasible. In addition, the proposed architecture can be applied to AR-type lattice filters, so that it may have several applications in adaptive signal processing. The presented filter architecture is useful from a hardware point of view because it facilitates an effective VLSI design of various adaptive lattice filters.

A new phase retrieval method using an active contour model (snake) for image reconstruction is proposed. The proposed method reconstructs a target image by retrieving the phase from the magnitude of its Fourier transform and the measured area of the image. In general, the measured area is different from the true area where the target image exists. Thus a snake, which can extract the shape of the target image, is utilized to renew the measured area. By processing this renewal iteratively, the area obtained by the snake converges to the true area and as a result the proposed method can accurately reconstruct a target image even when the measured area is different from the true area. Experimental results show the effectiveness of the proposed method.

In this paper, an ARMA order selection method is proposed with a fuzzy reasoning method. In order to identify the reference model with the ARMA model, we need to determine its ARMA order. A less or more ARMA order, other than a suitable order causes problems such as; lack of spectral information, increasing calculation cost, etc. Therefore, ARMA order selection is significant for a high accurate ARMA model identification. The proposed method attempts to select an ARMA order of a time-varying model with the following procedures: (1) Suppose the parameters of the reference model change slowly, by introducing recursive fuzzy reasoning method, the estimated order is selected. (2) By introducing a fuzzy c-mean clustering methed, the period of the time during which the reference model is changing is detected and the forgetting factor of the recursive fuzzy reasoning method is set. Further, membership functions used in our algorithm are original, which are realized by experiments. In this paper, experiments are documented in order to validate the performance of the proposed method.

This letter proposes a map-matching method for automotive navigation systems. The proposed method utilizes the innovation of the Kalman filter algorithm and can achieve more accurate positioning than the correlation method which is generally used for the navigation systems. In this letter, the performance of the proposed algorithm is verified by some simulations.

This paper presents a method of determining a fitness function in a genetic algorithm for routing the shortest route via several designated points. We can search for the optimum route efficiently by using the proposed fitness function and its validity is verified by applying it to the actual map data.

A large class of signals can be conveniently modeled by a stationary first-order Markoff process. This paper shows that for such a process the elements of the covariance matrix in the discrete Fourier transform domain can be calculated in closed form which facilitates a direct comparison of the transform with the discrete Karhunen-Loéve transform of KLT. A similar technique is applied to the analysis of the discrete consine transform or DCT. Both transforms are shown to be asymptotically equivalent to the KLT, i.e., they become equivalent to it as the block size or the number of sample points approaches infinity. Significant conclusions in this paper are that in the DCT domain the residual correlation is surprisingly smaller than in the DFT domain even for a nominal block size and that the decorrelation by the DCT is relatively immune to statistics change.

This paper presents a theoretical convergence analysis of a CORDIC-based adaptive ARMA lattice filter. In previous literatures, several investigation methods for adaptive lattice filters have been proposed; however, they are available only for AR-type filters. Therefore, we have developed a distinct technique that can reveal the convergence properties of the CORDIC ARMA lattice filter. The derived technique provides a quantitative convergence analysis, which facilitates an efficient hardware design for the filter. Moreover, our analysis technique can be applied to popular multiplier-based filters by slight modifications. Hence, the presented convergence analysis is significant as a leading attempt to investigate ARMA lattice filters.

This paper presents a new conic section extraction approach that can extract all conic sections (lines, circles, ellipses, parabolas and hyperbolas) simultaneously. This approach is faster than the conventional approaches with a computational complexity that is O(n), where n is the number of edge pixels, and is robust in the presence of moderate levels of noise. It has been combined with a classification tree to produce an offline character recognition system that is invariant to scale, rotation, and translation. The system was tested with synthetic images and with images scanned from real world sources with good results.