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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Image noise reducing method of non-down sampling contourlet transformation domain. Accelerating full wavefield inversion with nonstationary point-spread functions.

Curfelet description of the Hector Mine, California, earthquake, part I: The following references have been cited in the specification, either above or in the Annex: Additionally, implementations of the three-dimensional 3D discrete curvelet transform are also included.


New tight frames of curvelets and optimal representations of objects with piecewise-C 2 singularities. Multiscale and Multiresolution Methods, Each annulus is subdivided into prismoid regions tarnsforms two rectangular and four trapezoidal faces obeying the usual frequency parabolic scaling one long and two short directions. 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.


Both forward transforms are specified in closed form, and are invertible with inverse in transforns form for the wrapping version. The Annex forms an integral part of the specification as a whole. In particular, the cost of applying the adjoint is O n 2 log n flops, with n 2 being the number of pixels.

In the first example, the decay of the coefficients of the curvelet and various wavelet representations are compared on an image with curve-like singularities. Gobbers, Directional curveleg wavelet transforms: Digital Curvelet Transform via Wrapping Section 3. The original image is the seismogram used in the previous example FIG. The methods disclosed in this specification can be implemented on any processing unit that is capable of executing instructions of algorithms corresponding to the transforms set forth in this specification.

Restoration of cyrvelet frequency details while constructing the high resolution image C.

The interpolation step is organized so that it is obtained by solving a sequence of one-dimensional problems. One such digital transformation is based on unequally-spaced fast Fourier transforms USFFT while another is based on the wrapping of specially selected Fourier samples.

It is an object of the subject matter disclosed and claimed in this specification to provide fast and accurate discrete curvelet trwnsforms operating on digital data in order to realize the potential of curvelets and deploy this technology to a wide range of practical uses, such as image processing, data analysis, and scientific computing.


The FDCT via wrapping achieves machine accuracy because of the exact numerical tightness of the digital transform. Wave-character preserving prestack map migration using curvelets.

Fast Discrete Curvelet Transforms – CaltechAUTHORS

Math 57, This is especially challenging when one has incomplete data or in other words, when one cannot observe projections along every possible line but only along a given subset of such lines.

Stolk, Sparsity- and continuity-promoting seismic image recovery with curvelet frames. A few properties of the curvelet transform are listed below: This pyramid is nonstandard, however. 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.

Methods for performing fast discrete curvelet transforms of data.

This paper has 2, citations. The adjoint transformation shares all the basic properties of the forward transform.

US USB2 en Suresh BabuVijay ChandrasekharP. The two implementations essentially differ by the choice of spatial grid used to translate curvelets at each scale and angle.

Numerically, the non-aliased part amounts to about