The cubic-spline interpolation (CSI) scheme can be utilized to obtain a better quality reconstructed image. It is based on the least-squares method with cubic convolution interpolation (CCI) function. Within the parametric CSI scheme, it is difficult to determine the optimal parameter for various target images. In this paper, a novel method involving the concept of opportunity costs is proposed to identify the most suitable parameter for the CCI function needed in the CSI scheme. It is shown that such an optimal four-point CCI function in conjunction with the least-squares method can achieve a better performance with the same arithmetic operations in comparison with the existing CSI algorithm. In addition, experimental results show that the optimal six-point CSI scheme together with cross-zonal filter is superior in performance to the optimal four-point CSI scheme without increasing the computational complexity.

In this paper, it is shown that nonlinear image enhancement can be used to improve the quality of a blurred image by using the concept of opportunity cost with image classification. However, one observes from computer simulation that the values of clipping and scaling parameters are quite different in image enhancement for various blurred images. Therefore, one aim of this paper is to develop an effective image classification technique to decide the best combination of clipping and scaling parameters by the opportunity cost method for image enhancement. Experimental results show that the proposed opportunity cost method with image classification for the nonlinear image enhancement achieves a better subjective and objective image quality performance than the method using the opportunity cost without image classification and other nonlinear image enhancement methods.

It has been shown that the 2-D cubic spline interpolation (CSI) proposed by Truong et al. is one of the best algorithms for image resampling or compression. Such a CSI algorithm together with the image coding standard, e.g., JPEG, can be used to obtain a modified image codec while still maintaining a good quality of the reconstructed image for higher compression ratios. In this paper, a fast direct computation algorithm is developed to improve the computational efficiency of the original FFT-based 2-D CSI methods. In fact, this algorithm computes the 2-D CSI directly without explicitly calculating the complex division usually needed in the FFT or Winograd discrete Fourier transform (WDFT) algorithm. In addition, this paper describes a novel way to derivate the 2-D CSI from the 1-D CSI by using the row-column method. This new fast 2-D CSI provides a regular and simple structure based upon linear correlations. Therefore, it can be implemented by the use of a modification of Kung’s pipeline structure and is naturally suitable for VLSI implementations. Experimental results show that the proposed new fast 2-D CSI algorithm can achieve almost the same CSI performance with much fewer arithmetic operations in comparison with existing efficient algorithms.

It is well known that the B-spline filter can yield a very accurate algorithm for smoothing. In this paper, it is shown that a cubic B-spline filter can be used to improve the non-linear image enhancement method. In addition, a higher-frequency component is predicted to solve the blurred problem of an enlarged image. Furthermore, a novel non-linear image enhancement compensation algorithm is proposed to use for the video coding. Finally, a computer simulation shows that the proposed method yields a better quality of the decoded image than other non-linear enhancement methods.

In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2/sup m/-1 points over GF(2/sup m/), where 8/spl les/m/spl les/10. Using these transforms, together with the Berlekamp-Massey algorithm, the complexity of the transform-domain decoder for correcting both errors and erasures of the Reed-Solomon codes of block length 2/sup m/-1 over GF(2/sup m/) for 8/spl les/m/spl les/10 is reduced substantially from the previous time-domain decoder. A computer simulation verifies these new results.

Based on a cross-zonal filter in the two-dimensional (2-D) cubic-spline interpolation (CSI) and a symmetric extension method, an efficient algorithm is proposed for image coding. Experimental results show that the proposed method is superior in performance and yields a better quality of reconstructed image than other interpolation methods.

A new cubic convolution spline interpolation (CCSI )for both one-dimensional (1-D) and two-dimensional (2-D) signals is developed in order to subsample signal and image compression data. The CCSI yields a very accurate algorithm for smoothing. It is also shown that this new and fast smoothing filter for CCSI can be used with the JPEG standard to design an improved JPEG encoder-decoder for a high compression ratio.