7,963 research outputs found
GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging
Tomography has made a radical impact on diverse fields ranging from the study
of 3D atomic arrangements in matter to the study of human health in medicine.
Despite its very diverse applications, the core of tomography remains the same,
that is, a mathematical method must be implemented to reconstruct the 3D
structure of an object from a number of 2D projections. In many scientific
applications, however, the number of projections that can be measured is
limited due to geometric constraints, tolerable radiation dose and/or
acquisition speed. Thus it becomes an important problem to obtain the
best-possible reconstruction from a limited number of projections. Here, we
present the mathematical implementation of a tomographic algorithm, termed
GENeralized Fourier Iterative REconstruction (GENFIRE). By iterating between
real and reciprocal space, GENFIRE searches for a global solution that is
concurrently consistent with the measured data and general physical
constraints. The algorithm requires minimal human intervention and also
incorporates angular refinement to reduce the tilt angle error. We demonstrate
that GENFIRE can produce superior results relative to several other popular
tomographic reconstruction techniques by numerical simulations, and by
experimentally by reconstructing the 3D structure of a porous material and a
frozen-hydrated marine cyanobacterium. Equipped with a graphical user
interface, GENFIRE is freely available from our website and is expected to find
broad applications across different disciplines.Comment: 18 pages, 6 figure
Analysis of Three-Dimensional Protein Images
A fundamental goal of research in molecular biology is to understand protein
structure. Protein crystallography is currently the most successful method for
determining the three-dimensional (3D) conformation of a protein, yet it
remains labor intensive and relies on an expert's ability to derive and
evaluate a protein scene model. In this paper, the problem of protein structure
determination is formulated as an exercise in scene analysis. A computational
methodology is presented in which a 3D image of a protein is segmented into a
graph of critical points. Bayesian and certainty factor approaches are
described and used to analyze critical point graphs and identify meaningful
substructures, such as alpha-helices and beta-sheets. Results of applying the
methodologies to protein images at low and medium resolution are reported. The
research is related to approaches to representation, segmentation and
classification in vision, as well as to top-down approaches to protein
structure prediction.Comment: See http://www.jair.org/ for any accompanying file
Compressive auto-indexing in femtosecond nanocrystallography
Ultrafast nanocrystallography has the potential to revolutionize biology by
enabling structural elucidation of proteins for which it is possible to grow
crystals with 10 or fewer unit cells on the side. The success of
nanocrystallography depends on robust orientation-determination procedures that
allow us to average diffraction data from multiple nanocrystals to produce a
three dimensional (3D) diffraction data volume with a high signal-to-noise
ratio. Such a 3D diffraction volume can then be phased using standard
crystallographic techniques. "Indexing" algorithms used in crystallography
enable orientation determination of diffraction data from a single crystal when
a relatively large number of reflections are recorded. Here we show that it is
possible to obtain the exact lattice geometry from a smaller number of
measurements than standard approaches using a basis pursuit solver.Comment: Spence Festschrift on Ultramicroscop
Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
Euclidean distance matrices (EDM) are matrices of squared distances between
points. The definition is deceivingly simple: thanks to their many useful
properties they have found applications in psychometrics, crystallography,
machine learning, wireless sensor networks, acoustics, and more. Despite the
usefulness of EDMs, they seem to be insufficiently known in the signal
processing community. Our goal is to rectify this mishap in a concise tutorial.
We review the fundamental properties of EDMs, such as rank or
(non)definiteness. We show how various EDM properties can be used to design
algorithms for completing and denoising distance data. Along the way, we
demonstrate applications to microphone position calibration, ultrasound
tomography, room reconstruction from echoes and phase retrieval. By spelling
out the essential algorithms, we hope to fast-track the readers in applying
EDMs to their own problems. Matlab code for all the described algorithms, and
to generate the figures in the paper, is available online. Finally, we suggest
directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine
- change of title in the last revisio
PhaseMax: Convex Phase Retrieval via Basis Pursuit
We consider the recovery of a (real- or complex-valued) signal from
magnitude-only measurements, known as phase retrieval. We formulate phase
retrieval as a convex optimization problem, which we call PhaseMax. Unlike
other convex methods that use semidefinite relaxation and lift the phase
retrieval problem to a higher dimension, PhaseMax is a "non-lifting" relaxation
that operates in the original signal dimension. We show that the dual problem
to PhaseMax is Basis Pursuit, which implies that phase retrieval can be
performed using algorithms initially designed for sparse signal recovery. We
develop sharp lower bounds on the success probability of PhaseMax for a broad
range of random measurement ensembles, and we analyze the impact of measurement
noise on the solution accuracy. We use numerical results to demonstrate the
accuracy of our recovery guarantees, and we showcase the efficacy and limits of
PhaseMax in practice
The domain matrix method: a new calculation scheme for diffraction profiles
A new calculation scheme for diffraction profiles is presented that combines the matrix method with domain approaches. Based on a generalized Markov chain, the method allows the exact solution of the diffraction problem from any one-dimensionally disordered domain structure. The main advantage of this model is that a domain statistic is used instead of a cell statistic and that the domain-length distribution can be chosen independently from the domain-type stacking. A recursive relation is derived for the correlations between the domains and a double recursive algorithm, not reducible to a simpler one, is obtained as solution. The algorithm developed here is referred to as the domain matrix method. Results and applications of the new approach are discussed
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