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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To summarize, the curvelet transform is mathematically valid and it discrtee 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. The leftmost and rightmost pixels in a given row, or the top and bottom pixels in a given column, are considered immediate neighbors as much as ordinary adjacent pixels are. The key to higher-dimensional intermittency?

The method according to claim 13wherein the performing of the inverse discrete curvelet siscrete further comprises: The method according to claim 13wherein the inverse discrete curvelet transform runs in about O n 3 log n floating point operations for n by n discrette n Cartesian arrays, wherein n is a number of discrete information bits in a direction along an x, a y or a z axis. As before, this formula for b is understood when. The mathematics of computerized tomography. The second example is denoising.

## Fast Discrete Curvelet Transforms

It is sparse in the sense that the matrix entries in an arbitrary row or column decay nearly exponentially fast i. Much like in an orthonormal basis, an arbitrary function can be easily expanded as a series of curvelets see Equations 2. As is standard in scientific 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 as Riesz representers.

Wave-character preserving prestack map migration using curvelets. This specification discloses two distinct implementations of the curvelet transform which are faithful to the mathematical transformation outlined in Section 2 of the Annex. Vetterli, Contourlets, in Beyond WaveletsG. The parallelogram is the tile P j,l which contains the frequency support of the curvelet, whereas faxt gray parallelograms are the replicas resulting from periodization.

Redundant discrste transforms and their application for morphological component analysis. The method for transforming an image according to claim 1, wherein the division of the frequency plane comprises using a smooth partition of unity, or square-root thereof, made of overlapping indicators.

### Fast Discrete Curvelet Transforms – CaltechAUTHORS

Fourier Grenoble 48 In three dimensions, the step of performing the 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 bits in a direction along an x, a y or a z axis.

This specification discloses two distinct implementations of the curvelet transform which are faithful to the mathematical transformation outlined in Section 2 of the Annex. Modulation and equalization in an orthonormal time-frequency shifting communications system.

The method according to claim 13wherein the inverse discrete curvelet transform 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.

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. Each annulus is subdivided into trapezoidal regions. Schonewille, Nonuniform fast Fourier transform. The step of resampling within each trapezoidal or prismoidal region may further comprise the step of performing unequispaced Fast Fourier Transforms.

From This Paper Figures, tables, and topics from this paper. This issue is inevitable but minor, since it is equivalent to periodization in space where curvelets decay fast.

### Fast Discrete Curvelet Transforms – Semantic Scholar

The potential of FDCT’s is illustrated with several examples using the wrapping-based implementation. The method for manipulating data in a data processor may further comprise using a smooth partition of unity, or square-root thereof, made of overlapping indicators. The method according to claim 6 being an isometry in exact arithmetic.

What is lost in terms of aliasing? The following references have been cited in the specification, either above or in the Annex: The Annex forms an integral part of the specification as a whole.

The first input image, shown in FIG. Cirvelet curvelets, curvelet coefficients Equations 2. The method for manipulating data in a data processor may be one in which the transform is invertible by means of an inverse transform. Vetterli, The contourlet transform: Shiftable multi-scale transforms [or what’s wrong with orthonormal wavelets].

The method according to claim 1wherein the transforming of the image comprises identifying transients or salient features in the plurality of image pixel data. The step of performing the inverse transform may further comprise c shearing the array of the Fourier-transformed data at each scale and angle onto a trapezoidal or prismoidal grid; d resampling each sheared data onto a Cartesian grid; e windowing by the corresponding indicator; f summing the contributing at each scale and angle; g performing an inverse Fourier transform of the sum.

The new mathematical architecture suggests innovative algorithmic strategies, and provides the opportunity to improve upon earlier implementations. The method according to claim 1wherein the transforming of the image is used to conduct numerical simulations of partial differential equations.