Kristian Sandberg

Methods for image segmentation in cellular tomography.

Publisher Summary The goal for image segmentation involves decomposing an image into its constituent parts. This chapter discusses and illustrates some of the challenges for constructing robust and efficient segmentation methods for cellular tomography. It also discusses approaches for evaluating the usability of segmentation methods and suggests a possible approach for quantifying the accuracy of segmentation algorithms. The chapter includes a review of several existing methods for denoising, contrast enhancement, and segmentation. It is noted that some frequently suggested methods are often impractical for real data sets due to the computational complexity and difficulty in finding appropriate algorithm parameters. The segmentation methods based only on intensity and contrast have problems in detecting thin, elongated structures. Therefore, the chapter proposes the use of geometrical information, such as correlation among orientations, to detect membranes and microtubules. It also outlines a new orientation-based segmentation method and demonstrates this method on real tomograms.

Full-wave-equation depth extrapolation for migration

Most of the traditional approaches to migration by downward extrapolation suffer from inaccuracies caused by using one-waypropagation,bothintheconstructionofsuchpropagatorsinavariablebackgroundandthesuppressionofpropagatingwavesgeneratedby,e.g.,steepreflectors.Wepresenta new mathematical formulation and an algorithm for downward extrapolation that suppress only the evanescent waves. Weshowthatevanescentwavemodesareassociatedwiththe positive eigenvalues of the spatial operator and introduce spectralprojectorstoremovethesemodes,leavingallpropagating modes corresponding to nonpositive eigenvalues intact. This approach suppresses evanescent modes in an arbitrarylaterallyvaryingbackground.Ifthebackgroundvelocityisonlydepthdependent,thenthespectralprojectormaybe applied by using the fast Fourier transform and a filter in the Fourier domain. In computing spectral projectors, we use an iterationthatavoidstheexplicitconstructionoftheeigensystem.Moreover,weusearepresentationofmatricesleadingto fast matrix-matrix multiplication and, as a result, a fast algorithmnecessaryforpracticalimplementationofspectralprojectors. The overall structure of the migration algorithm is similar to survey sinking with an important distinction of using a new method for downward continuation. Using a blurredversionofthetruevelocityasabackground,steepreflectorscanbeimagedina2DsliceoftheSEG-EAGEmodel.

ODE solvers using band-limited approximations

We use generalized Gaussian quadratures for exponentials to develop a new ODE solver. Nodes and weights of these quadratures are computed for a given bandlimit c and user selected accuracy @e, so that they integrate functions e^i^b^x, for all |b|=

Full-wave-equation Depth Migration Using Multiple Reflections

We present a migration method in the temporal frequency domain that can propagate both downgoing and upgoing waves. The method can handle arbitrary velocity model, and we demonstrate its ability to image overturned events and steep reflectors. Our algorithm has the advantage of migrating the data sequentially in depth and frequency, leading to significant advantages compared to Reverse Time Migration when combined with migration velocity analysis. We also show that the method can easily generate offset and angle gathers.

Acoustic And Elastic Modeling Using Bases For Bandlimited Functions

In this paper we describe a novel algorithm for solving acoustic and elastic wave equations. The algorithm utilizes prolate spheroidal wavefunctions for representing bandlimited functions. Key features of the method are high accuracy, elimination of numerical dispersion, and close to optimal sampling rates. Numerical results in two and three dimensions are presented which demonstrate the accuracy of the method and its ability to handle complex media such as the SEG salt model.