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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A few properties of the curvelet transform are listed below: Both forward transforms are specified in closed form, and are invertible with inverse in closed form for the wrapping version.

### Fast Discrete Curvelet Transforms – Semantic Scholar

The second example is denoising. New tight frames of curvelets and optimal representations of objects with piecewise-C 2 singularities. These are now six components corresponding to the six faces of the cube. The step of resampling sheared data may comprise performing inverse unequispaced Fast Fourier transforms. The step of unwrapping data onto a trapezoidal or prismoidal region may comprise making use of periodization to extend Fourier samples inside the trapezoidal or prismoidal region.

Hermann, Seismic denoising with unstructured curvelets, submitted, Accordingly, an embodiment of the invention is directed to a method for manipulating data in a data processor, comprising performing a discrete curvelet transform on the data.

Each CG iteration is effected by a series of one dimensional processes which, thanks to the special structure of the Gram matrix, can be accelerated as we will see in the next section. The method for manipulating data in a data processor, comprising performing a discrete curvelet transform on the data may be one in which the step for performing the transform further comprises returning a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter.

Harmonic analysis of neural networks. Fast wavelet transforms and numerical algorithms. To summarize, the curvelet transform is mathematically valid and it has a very promising potential in traditional and perhaps less traditional application areas for wavelet-like ideas such as image processing, data analysis, and scientific computing. Equipped with this definition, the architecture of the fast digital curvelet transform by wrapping is generally as follows: Showing of 1, extracted citations.

The step of performing the inverse transform may be one in which the inversion algorithm runs in about O n 2 log n floating point operations for n by n Cartesian arrays, wherein n is a number of discrete information bits in a direction along an x or a y axis. References Publications referenced by this paper. To compensate for the redundancy of the curvelet transform and display a meaningful comparison, a fraction of the entries of the curvelet coefficient table are extracted so that the number of curvelet and wavelet coefficients is identical.

As is standard in siscrete computations, these digital waveforms which are implicitly defined by the algorithms are never actually built; formally, they are the rows of the matrix representing the linear transformation and are also known idscrete Riesz representers.

Formi, Detecting cosmological non-Gaussian signatures by multi-scale methods. In the field of scientific computing, wavelets and related multiscale methods sometimes allow for the speeding up of fundamental scientific computations such as in the numerical evaluation of the solution of partial differential equations.

While several illustrative embodiments of the invention have been shown and described in the above description, numerous variations and alternative embodiments will idscrete to those skilled in the art and it should be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.

This method may comprise the steps of a representing the data in the frequency space or Fourier domain by means of a Fourier transform; b dividing the Fourier transform of the data into dyadic ddiscrete based on concentric squares for two-dimensional data or concentric cubes for three-dimensional data and each annulus is subdivided into trapezoidal regions for two-dimensional data or prismoids for three-dimensional data. The method according to claim 1, wherein the performing of the discrete curvelet transform runs in O n 3 log n floating point operations for n by n by n Cartesian arrays, wherein n is the number of discrete information dast in a direction along an x, a y, or a z axis.

## CROSS-REFERENCE TO RELATED APPLICATION

Wave-character preserving prestack map migration using transformms. Fast Fourier transforms for nonequispaced data. The method according to claim 1, wherein the transforming of the image is used to conduct numerical simulations of partial differential equations. The resemblance of the formula given above in the above paragraph with a standard 2D inverse FFT is in that respect only formal.

Technical report, California Trajsforms of Technology, Frequency space is divided into dyadic annuli based on concentric squares. The processing units and computers fat them are designed to execute software under the control of an operating system. Curvelte new FDCT’s run in O n 2 log n flops floating point operations for n by n Cartesian arrays, and are also invertible, with rapid inversion algorithms of about the same complexity.

Informally speaking, one can think of curvelets as near-eigen functions of the solution operator to a large class of hyperbolic differential equations. The transforms are cache-aware: The following references have been cited in the specification, either above or in the Annex: System and method for two-dimensional equalization in an orthogonal time frequency space communication system.

For a given scale, this corresponds only to two Cartesian sampling grids, one for all angles in the East-West quadrants, and one for the North-South quadrants.

## Satellite image fusion using Fast Discrete Curvelet Transforms

Soon after their introduction, researchers developed numerical algorithms for their implementation see references 37 and 18and scientists have started to report on a series of practical successes see, for example, references 39, 38, 27, 26, and discrtee In these challenging setups, the FDCT may be used to separate the image of interest from noise and clutters and provide sharp reconstructions of selected image features.

Each annulus is subdivided into prismoid regions having two rectangular and four trapezoidal faces obeying the usual frequency parabolic scaling one long and two short directions. For example, a remarkable property is that curvelets faithfully model the geometry of wave propagation.

Three examples of such problems are:. Citation Statistics 2, Citations 0 ’07 ’10 ’13 ’16 ‘ Curvelets also have special microlocal features which make them especially adapted to certain reconstruction problems with missing trannsforms.

From This Paper Figures, tables, and topics from this paper. Section 6 of the Annex details some of the properties of this transform, namely, 1 it is an isometry, hence the inverse transform can simply be computed as the adjoint, and 2 it is faithful to the continuous transform.

Recall that the other potential source of error, spatial sampling, is not an issue here since curvelets are nearly bandlimited. This phenomenon has immediate applications in approximation theory and in statistical estimation. Hence, the wrapping transformation is a simple re-indexing of the data.

ChaudhariShrinvas P. Redundant multiscale transforms and their application for morphological component analysis. The output may be thought of as a collection of coefficients c D j,l,k obtained by Equation 3.

More information and software credits. Subject matter disclosed in this specification was supported at least in part through governmental grants no. Both forward transforms are specified in closed form, and are invertible with inverse in closed form for the wrapping version.