Abstract This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform [12, 10] in two and three dimensions. The first digital transformation is based on unequally-spaced fast Fourier transforms USFFT while the second is based on the wrapping of specially selected Fourier samples. The two implementations essentially differ by the choice of spatial grid used to translate curvelets at each scale and angle. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. And both implementations are fast in the sense that they run in O n 2 log n flops for n by n Cartesian arrays; in addition, they are also invertible, with rapid inversion algorithms of about the same complexity.
|Country:||Moldova, Republic of|
|Published (Last):||17 October 2013|
|PDF File Size:||5.36 Mb|
|ePub File Size:||12.2 Mb|
|Price:||Free* [*Free Regsitration Required]|
The first digital transformation is based on unequally spaced fast Fourier transforms, while the second is based on the wrapping of specially selected Fourier samples. The two implementations essentially differ by the choice of spatial grid used to translate curvelets at each scale and angle.
Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Our digital transformations improve upon earlier implementations—based upon the first generation of curvelets—in the sense that they are conceptually simpler, faster, and far less redundant. Crossref An edge driven wavelet frame model for image restoration. Applied and Computational Harmonic Analysis , Signal Processing: Image Communication 84, Crossref Segmentation of scanning tunneling microscopy images using variational methods and empirical wavelets.
Pattern Analysis and Applications , Geophysical Prospecting Crossref Surface defect identification of aluminium strips with non-subsampled shearlet transform. Optics and Lasers in Engineering , IRBM , Crossref An automated computer-aided diagnosis system for classification of MR images using texture features and gbest-guided gravitational search algorithm. Biocybernetics and Biomedical Engineering. Crossref An accelerated proximal gradient algorithm for source-independent waveform inversion.
Journal of Applied Geophysics, Crossref A novel thresholding method for simultaneous seismic data reconstruction and denoising. Crossref Coding Theory. Crossref Application of the curvelet transform to synthetic and real magnetic data. Exploration Geophysics , Crossref Off-the-grid vertical seismic profile data regularization by a compressive sensing method. Crossref Effective curvelet-based facial expression recognition using graph signal processing.
Signal, Image and Video Processing , Entropy , Crossref A fast RetinaNet fusion framework for multi-spectral pedestrian detection. Crossref Image restoration using hybrid features improvement on morphological component analysis. Journal of Electronic Science and Technology, Crossref A curvelet method for numerical solution of partial differential equations.
Applied Numerical Mathematics , Crossref A hybrid regularization approach for random vector functional-link networks.
Expert Systems with Applications , Crossref Fast curvelet transform through genetic algorithm for multimodal medical image fusion.
Soft Computing , Crossref Unsupervised machine learning for waveform extraction in microseismic denoising. Journal of Applied Geophysics , Crossref Three-dimensional curvelet-based dictionary learning for speckle noise removal of optical coherence tomography. Biomedical Optics Express , Crossref Fusion of geophysical images in the study of archaeological sites. Archaeological Prospection Pure and Applied Geophysics Crossref Self-training and learning the waveform features of microseismic data using an adaptive dictionary.
Mathematical Preliminaries. Advanced Techniques for Audio Watermarking, Cardiovascular Engineering, Crossref Tight framelets and fast framelet filter bank transforms on manifolds.
Crossref Progressive denoising of seismic data via robust noise estimation in dual domains. Medical Physics , Crossref A new sparse representation framework for compressed sensing MRI.
Knowledge-Based Systems , Crossref Detection in seismic data using curvelet transform and tensor-based elliptical adaptive structuring elements.
Crossref An anti-aliasing POCS interpolation method for regularly undersampled seismic data using curvelet transform. Innovative Data Communication Technologies and Application, IEEE Access 8, Pure and Applied Geophysics , Machine Intelligence and Signal Processing, Computer Vision and Image Processing, Real-time video segmentation using a vague adaptive threshold.
Hybrid Computational Intelligence, Frontiers in Bioengineering and Biotechnology 8. Futuristic Trends in Networks and Computing Technologies, Digital Signal Processing 95, Crossref On the design of multi-dimensional compactly supported Parseval framelets with directional characteristics.
Linear Algebra and its Applications , Crossref Emplacement and 3D geometry of crustal-scale saucer-shaped intrusions in the Fennoscandian Shield. Scientific Reports Crossref An efficient wavelet and curvelet-based PET image denoising technique.
International Journal of Modern Physics C , Crossref Defect detection of optical elements surfaces using curvelet transform. Crossref Random noise suppression of seismic data by time—frequency peak filtering with variational mode decomposition. Crossref Desert low-frequency noise suppression by using adaptive DnCNNs based on the determination of high-order statistic.
Geophysical Journal International , Applied Sciences , Crossref Contour detection based on anisotropic edge strength and hierarchical superpixel contrast. Crossref A multi-algorithm block fusion method based on set-valued mapping for dual-modal infrared images.
Crossref Simultaneous interpolation and denoising based on a modified thresholding method. Studia Geophysica et Geodaetica , Crossref Reconstruction of compressively sampled MR images based on a local shrinkage thresholding algorithm with curvelet transform. Crossref Power shrinkage—curvelet domain image denoising using a new scale-dependent shrinkage function.
Crossref Application of fast curvelet Tsallis entropy and kernel random vector functional link network for automated detection of multiclass brain abnormalities. Computerized Medical Imaging and Graphics 77, Crossref Robust joint representation with triple local feature for face recognition with single sample per person.
Crossref Medical image denoising using multi-resolution transforms. Measurement , Symmetry , Crossref MJaya-ELM: A Jaya algorithm with mutation and extreme learning machine based approach for sensorineural hearing loss detection.
Applied Soft Computing 83, Crossref Investigation of moving objects through atmospheric turbulence from a non-stationary platform. Crossref Improving image steganalyser performance through curvelet transform denoising. Cluster Computing S5, Crossref Automatic high-resolution microseismic event detection via supervised machine learning. Crossref Compressive least-squares migration with on-the-fly Fourier transforms. Crossref Gaussian beam reconstruction of seismic data.
Multimedia Tools and Applications , Crossref Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition. Journal of Fluid Mechanics , Crossref Medical image segmentation using fast discrete curvelet transform and classification methods for MRI brain images. Multimedia Tools and Applications
Multiscale Modeling & Simulation
Fast Discrete Curvelet Transforms