High-dimensional wave atoms and compression of seismic data sets

Wave atoms are a low-redundancy alternative to curvelets, suitable for high-dimensional seismic data processing. This abstract extends the wave atom orthobasis construction to 3D, 4D, and 5D Cartesian arrays, and parallelizes it in a sharedmemory environment. An implementation of the algorithm for NVIDIA CUDA capable graphics processing units (GPU) is also developed to accelerate computation for 2D and 3D data. The new transforms are benchmarked against the Fourier transform for compression of data generated from synthetic 2D and 3D acoustic models.TOTAL (Firm)National Science Foundation (U.S.)Alfred P. Sloan Foundatio

High-dimensional wave atoms and compression of seismic datasets

Wave atoms are a low-redundancy alternative to curvelets, suitable for high-dimensional seismic data processing. This abstract extends the wave atom orthobasis construction to 3D, 4D, and 5D Cartesian arrays, and parallelizes it in a shared-memory environment. An implementation of the algorithm for NVIDIA CUDA capable graphics processing units (GPU) is also developed to accelerate computation for 2D and 3D data. The new transforms are benchmarked against the Fourier transform for compression of data generated from synthetic 2D and 3D acoustic models.National Science Foundation (U.S.); Alfred P. Sloan Foundatio

Curvelets and Ridgelets

International audienceDespite the fact that wavelets have had a wide impact in image processing, they fail to efficiently represent objects with highly anisotropic elements such as lines or curvilinear structures (e.g. edges). The reason is that wavelets are non-geometrical and do not exploit the regularity of the edge curve. The Ridgelet and the Curvelet [3, 4] transforms were developed as an answer to the weakness of the separable wavelet transform in sparsely representing what appears to be simple building atoms in an image, that is lines, curves and edges. Curvelets and ridgelets take the form of basis elements which exhibit high directional sensitivity and are highly anisotropic [5, 6, 7, 8]. These very recent geometric image representations are built upon ideas of multiscale analysis and geometry. They have had an important success in a wide range of image processing applications including denoising [8, 9, 10], deconvolution [11, 12], contrast enhancement [13], texture analysis [14, 15], detection [16], watermarking [17], component separation [18], inpainting [19, 20] or blind source separation[21, 22]. Curvelets have also proven useful in diverse fields beyond the traditional image processing application. Let’s cite for example seismic imaging [10, 23, 24], astronomical imaging [25, 26, 27], scientific computing and analysis of partial differential equations [28, 29]. Another reason for the success of ridgelets and curvelets is the availability of fast transform algorithms which are available in non-commercial software packages following the philosophy of reproducible research, see [30, 31]

PAPR FOR OFDM SYSTEM BASED ON FAST DISCRETE CURVELET TRANSFORM

Orthogonal Frequency-Division Multiplexing (OFDM) is an attractive transmission technique for high-bit-rate communication systems. However, high Peak to Average Power Ratio (PAPR) of transmitted signals is a major shortcoming for Multi-Carrier Modulation (MCM) system such as the OFDM system. Traditional OFDM implementations use common Fourier filters for data modulation and demodulation via the Inverse Fast Fourier Transform (IFFT) and the FFT operations respectively, in this paper the Fast Discrete Curvelet Transform (FDCT) is proposed for OFDM in order to reduce the PAPR. The software CurveLab, used in this work is available at http://www.curvelet.org. The proposed system used FDCT via both Unequispaced Fast Fourier Transform (USFFT) and Wrapping. In terms of PAPR, the results show that both transforms used in this work gives better PAPR results, FDCT via USFFT and FDCT via Wrapping are given approximately about 7.7 dB reduction compared to traditional OFDM. Moreover, the results show that the BER performance of the considered system nearly matches the theoretical BPSK BER performance in an Additive White Gaussian Noise (AWGN) channel

Recursive Imaging with Multiply-Scattered Waves Using Partial Image Regularization: A North Sea Case Study

As more resources are directed toward reverse-time migration an accurate velocity model, including strong reflectors, is necessary to form a clear image of the subsurface. This is of particular importance in the vicinity of salt, where singly-scattered waves are often not ideal for imaging the salt flanks. This has led to interest in processing doubly-scattered waves (also called duplex or prismatic waves) for imaging salt flanks and thus improving the location of salt boundaries in a velocity model. We present a case study in which we use doubly-scattered waves in a two-pass one-way method to image salt flanks in a North Sea data set. By working in the one-way framework we are able to separately construct images with singly, doubly, and triply scattered waves. We illustrate a multi-step imaging process that includes multiply-scattered waves by using an imaged reflector to fix one (or more) of the scattering points, allowing for multiply-scattered energy from several reflectors, potentially with poor continuity, to be included without picking each reflector individually. With this method we are able to image the flank of a North Sea salt body.Norwegian State Oil CompanyNorwegian Research CouncilGeo-Mathematical Imaging GroupTOTAL (Firm)Massachusetts Institute of Technology. Earth Resources Laborator