Singularity-Exponent-Domain Image Feature Transform.

Combining the generalized fractal theory and the time-frequency distribution, the image feature decomposition in the singularity exponent domain is studied in this paper. With the theoretical derivation and quantitative analysis, the singularity-exponent-domain image feature transform (SIFT) method is proposed to analyze and process images from new feature dimensions. If one derives from the generalized fractal characteristics of the image, the two-dimensional frequency variables of the 2D time-frequency transform of the image can be used to estimate the two-dimensional singularity power spectrum (SPS) in the space dimension. As a consequence, it leads to the SPS distribution of the original image in the spatial domain, i.e., SIFT images. Based on the SIFT, the feature transform images with different singularity exponent and feature curves of singularity power spectrum with respect to different physical regions can thus be obtained. The SIFT is rigorously derived from the 2D-SPS and the Pseudo Wigner-Ville distribution (PWVD). In addition, the feature images based on the SIFT is proved to be the SNR independence in the GWN background. In order to validate the effectiveness of feature extraction, the proposed methodology is tested on the breast ultrasound images, the visual images, and the synthetic aperture radar (SAR) images. Furthermore, the SAR target detection method based on the SIFT images is proposed, and the experiment results indicate that the proposed algorithm is superior in performance to the traditional CFAR or 2D-SPS method. In fact, this new SIFT is promising to provide a technical approach for image feature extraction, target detection, and recognition.

Reconstruction of Single Image from Multiple Blurry Measured Images.

The problem of blind image recovery using multiple blurry images of the same scene is addressed in this paper. To perform blind deconvolution, which is also called blind image recovery, the blur kernel and image are represented by groups of sparse domains to exploit the local and nonlocal information such that a novel joint deblurring approach is conceived. In the proposed approach, the group sparse regularization on both the blur kernel and image is provided, where the sparse solution is promoted by -norm. In addition, the reweighted data fidelity is developed to further improve the recovery performance, where the weight is determined by the estimation error. Moreover, to reduce the undesirable noise effects in group sparse representation, distance measures are studied in the block matching process to find similar patches. In such a joint deblurring approach, a more sophisticated two-step interactive process is needed in which each step is solved by means of the well-known split Bregman iteration algorithm, which is generally used to efficiently solve the proposed joint deblurring problem. Finally, numerical studies, including synthetic and real images, demonstrate that the performance of this joint estimation algorithm is superior to the previous state-of-the-art algorithms in terms of both objective and subjective evaluation standards. The recovery results of real captured images using unmanned aerial vehicles are also provided to further validate the effectiveness of the proposed method.

Novel approaches to the parametric cubic-spline interpolation.

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.

Simplified 2-D cubic spline interpolation scheme using direct computation algorithm.

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.