The ridgelet transform was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. We propose an orthonormal version of the ridgelet transform for discrete and finite-size images. Our construction uses the finite Radon transform (FRAT) as a building block. To overcome the periodization effect of a finite transform, we introduce a novel ordering of the FRAT coefficients. We also analyze the FRAT as a frame operator and derive the exact frame bounds. The resulting finite ridgelet transform (FRIT) is invertible, nonredundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional and orthonormal bases for images. Numerical results show that the FRIT is more effective than the wavelet transform in approximating and denoising images with straight edges.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1109/TIP.2002.806252 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Image denoising method integrating ridgelet transform and improved wavelet threshold.
PLoS One
September 2024
College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, China.
In the field of image processing, common noise types include Gaussian noise, salt and pepper noise, speckle noise, uniform noise and pulse noise. Different types of noise require different denoising algorithms and techniques to maintain image quality and fidelity. Traditional image denoising methods not only remove image noise, but also result in the detail loss in the image.
View Article and Find Full Text PDFImproving the Method of Short-term Forecasting of Electric Load in Distribution Networks using Wavelet transform combined with Ridgelet Neural Network Optimized by Self-adapted Kho-Kho Optimization Algorithm.
Heliyon
April 2024
Department of Electrical Engineering, Kerman Branch, Islamic Azad University, Kerman, Iran.
This paper proposes a new method for short-term electric load forecasting using a Ridgelet Neural Network (RNN) combined with a wavelet transform and optimized by a Self-Adapted (SA) Kho-Kho algorithm (SAKhoKho). The aim of this method is to improve the accuracy and reliability of electric load forecasting, which is essential for the planning and operation of competitive electrical networks. The proposed method uses the Wavelet Transform (WT) to decompose the load data into different frequency components and applies the RNN to each component separately.
View Article and Find Full Text PDFEmpirical Curvelet-ridgelet Wavelet Transform for Multimodal Fusion of Brain Images.
Curr Med Imaging
January 2024
Department of Electronics and Communication Engineering, Jaypee University of Information Technology, Solan, Himachal Pradesh, India.
Background: Empirical curvelet and ridgelet image fusion is an emerging technique in the field of image processing that aims to combine the benefits of both transforms.
Objective: The proposed method begins by decomposing the input images into curvelet and ridgelet coefficients using respective transform algorithms for Computerized Tomography (CT) and magnetic Resonance Imaging (MR) brain images.
Methods: An empirical coefficient selection strategy is then employed to identify the most significant coefficients from both domains based on their magnitude and directionality.
Meningioma brain tumor detection and classification using hybrid CNN method and RIDGELET transform.
Sci Rep
September 2023
Department of Mathematics and Computer Science, Molloy University, Rockville Centre, NY, USA.
The detection of meningioma tumors is the most crucial task compared with other tumors because of their lower pixel intensity. Modern medical platforms require a fully automated system for meningioma detection. Hence, this study proposes a novel and highly efficient hybrid Convolutional neural network (HCNN) classifier to distinguish meningioma brain images from non-meningioma brain images.
View Article and Find Full Text PDFLocal-Ternary-Pattern-Based Associated Histogram Equalization Technique for Cervical Cancer Detection.
Diagnostics (Basel)
February 2023
Amrita School of Computing, Amrita Vishwa Vidyapeetham, Amaravati Campus, Amaravati 522503, India.
Every year, cervical cancer is a leading cause of mortality in women all over the world. This cancer can be cured if it is detected early and patients are treated promptly. This study proposes a new strategy for the detection of cervical cancer using cervigram pictures.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!