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Oct 10, Fast Discrete Curvelet Transforms. Article (PDF Available) in SIAM Journal on Multiscale Modeling and Simulation 5(3) · September with. Satellite image fusion using Fast Discrete Curvelet Transforms. Abstract: Image fusion based on the Fourier and wavelet transform methods retain rich. Nov 23, Fast digital implementations of the second generation curvelet transform for use in data processing are disclosed. One such digital.

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Satellite image fusion using Fast Discrete Curvelet Transforms

Digital implementation of ridgelet packets, Beyond WaveletsJ. Technical Report, Stanford University, The method according to claim dixcretewherein the resampling of the sheared data comprises performing inverse unequispaced Fast Fourier transforms.

This is a sampling issue in which, if a fine-scale curvelet is sampled too coarsely, cast pixelization will make it look like a checkerboard and it will not be clear in which direction it oscillates anymore. This sampling in frequency is the only distortion that curvelets incur in the digital transforms. Recovering edges in ill-posed inverse problems: Just as the wavelet transform has been deployed a countless number of times in many fields of science and technology, fast digital curvelet transforms may be expected to be widely applicable.

For example, a remarkable property is that curvelets faithfully model the geometry of wave propagation. Methods for subsurface parameter estimation in full wavefield inversion and reverse-time migration.

Abstract This paper describes two digital implementations of a transcorms mathematical transform, namely, the second generation curvelet transform in two and three dimensions. The following references have been cited in the specification, either above or in the Annex: Wrapping graphics Cartesian closed category.

Shiftable multi-scale transforms [or what’s wrong with orthonormal wavelets].


The interpolation step is organized so that it is obtained by solving a sequence of one-dimensional problems. To realize this potential though, and deploy this technology to a wide range of problems, fast and accurate discrete curvelet transforms operating on digital data are needed. The following references have been cited in the specification, ciscrete above or in the Annex:. Curveleh, Sparsity- and continuity-promoting seismic image recovery with curvelet frames.


By construction, a substantial number of basis functions appear to be supported on two or more very distant regions of the image, because they overlap the image boundary and get copied by periodicity. It is sparse in the sense that the matrix entries in an arbitrary row or column decay nearly exponentially fast i.

Looking at the flow of the algorithm for the USFFT set forth above, the first and the last steps may be seen to be easily invertible by means of FFT’s. Curvelets are especially well-adapted to simultaneously represent the solution operators to large classes of wave equations and the wavefields that are solutions to those equations.

Frequency space is divided into dyadic annuli based on concentric squares. The step of wrapping data within each trapezoidal or prismoidal region may comprise making use of periodization to extend Fourier samples inside the rectangular or parallelepipedal region. In the frequency domain, they are sharply localized.

The step of performing the inverse transform may comprise a taking as input the table of digital curvelet curevlet b performing a Fast Fourier transform of the coefficients at each scale and angle. It is possible to design an algorithm which, for practical purposes, is exact and takes O n 2 log n flops for computation, and requires O n 2 storage, where n 2 is the number of pixels.

In scientific computing, the fast digital curvelet transform may be used for speeding up fundamental computations; the numerical propagation of waves in inhomogeneous media is of special interest.

In particular, the cost of applying the adjoint is O n 2 log n flops, with n 2 being the number of pixels. Iterative tomographic image reconstruction using Fourier-based forward and back-projectors. This specification discloses two distinct implementations of the curvelet transform which are faithful to the mathematical transformation outlined in Section 2 of the Annex.


In three dimensions, The method according to claim 13 in which the inversion algorithm runs in about O n 3 log n floating point operations for n by n by n Cartesian arrays, wherein n is a number of discrete information bits in a direction along an x, a y or a z axis.

Wavelets perform well only at linear features but not at non linear discontinuities because they do not use the geometric properties of structures. LakshmiVinay K. By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy PolicyTerms of Serviceand Dataset License. The new FDCT’s are based on the curvelet transform described in reference Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter.

Fast Discrete Curvelet Transforms – CaltechAUTHORS

Hermann, Seismic denoising with unstructured curvelets, submitted, Curvelets may also be a very significant tool for the analysis and the computation of partial differential equations. The method according to claim 1, wherein the transforming of the image is used to solve inverse problems. The method according to claim 1wherein the transforming of the image comprises cast transients or salient features in the plurality of image pixel data.

Next Patent Methods for spectral A Directional Multiresolution Image Representation On the fast Fourier transform of functions with singularities. Such variations and alternative embodiments are contemplated, and can be made, without departing from the scope of the invention as defined in the appended claims.