Ripplet transform and its extension to Boehmians

First, we correct the mistake in the inversion theorem of the ripplet transform in the literature. Next, we prove a convolution theorem for the ripplet transform and extend the ripplet transform as a continuous, linear, injective mapping from a suitable Boehmian space into another Boehmian space.

Ripplet-Transform-based Cycle Spinning Denoising and Fuzzy-CLA Segmentation of Retinal Images for Accurate Hard Exudates and Lesion Detection

Aims: Digital retinal images are commonly used for hard exudates and lesion detection. These images are rarely noiseless and therefore before any further processing they should be underwent noise removal. Background: An efficient segmentation method is then needed to detect and discern the lesions from the retinal area. Objective: In this paper, a hybrid method is presented for digital retinal image processing for diagnosis and screening purposes. The aim of this study is to present a supervised/semi-supervised approach for exudate detection in fundus images and also to analyze the method to find the optimum structure. Methods: Ripplet transform and cycle spinning method is first used to remove the noises and artifacts. Results: The noises may be normal or any other commonly occurring forms such as salt and pepper. The image is transformed into fuzzy domain after it is denoised. Conclusion: A cellular learning automata model is used to detect any abnormality on the image which is related to a lesion. The automaton is created with an extra term as the rule updating term to improve the adaptability and efficiency of the cellular automata.Three main statistical criteria are introduced as the sensitivity, specificity and accuracy. A number of 50 retinal images with visually detection hard exudates and lesions are the experimental dataset for evaluation and validation of the method.

Multifocus image fusion based on coefficient significance of redundant discrete wavelet transform

Purpose This study aims to obtain the more precise decision map to fuse the source images by Coefficient significance method. In the area of multifocus image fusion, the better decision map is very important the fusion results. In the processing of distinguishing the well-focus part with blur part in an image, the edge between the parts is more difficult to be processed. Coefficient significance is very effective in generating the better decision map to fuse the multifocus images. Design/methodology/approach The energy of Laplacian is used in the approximation coefficients of redundant discrete wavelet transform. On the other side, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient. Findings Due to the shift-variance of the redundant discrete wavelet and the effectiveness of fusion rule, the presented fusion method is superior to the region energy in harmonic cosine wavelet domain, pixel significance with the cross bilateral filter and multiscale geometry analysis method of Ripplet transform. Originality/value In redundant discrete wavelet domain, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient of source images.