11,643 research outputs found
On random tomography with unobservable projection angles
We formulate and investigate a statistical inverse problem of a random
tomographic nature, where a probability density function on is
to be recovered from observation of finitely many of its two-dimensional
projections in random and unobservable directions. Such a problem is distinct
from the classic problem of tomography where both the projections and the unit
vectors normal to the projection plane are observable. The problem arises in
single particle electron microscopy, a powerful method that biophysicists
employ to learn the structure of biological macromolecules. Strictly speaking,
the problem is unidentifiable and an appropriate reformulation is suggested
hinging on ideas from Kendall's theory of shape. Within this setup, we
demonstrate that a consistent solution to the problem may be derived, without
attempting to estimate the unknown angles, if the density is assumed to admit a
mixture representation.Comment: Published in at http://dx.doi.org/10.1214/08-AOS673 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A method for delineation of bone surfaces in photoacoustic computed tomography of the finger
Photoacoustic imaging of interphalangeal peripheral joints is of interest in
the context of using the synovial membrane as a surrogate marker of rheumatoid
arthritis. Previous work has shown that ultrasound produced by absorption of
light at the epidermis reflects on the bone surfaces within the finger. When
the reflected signals are backprojected in the region of interest, artifacts
are produced, confounding interpretation of the images. In this work, we
present an approach where the photoacoustic signals known to originate from the
epidermis, are treated as virtual ultrasound transmitters, and a separate
reconstruction is performed as in ultrasound reflection imaging. This allows us
to identify the bone surfaces. Further, the identification of the joint space
is important as this provides a landmark to localize a region-of-interest in
seeking the inflamed synovial membrane. The ability to delineate bone surfaces
allows us not only to identify the artifacts, but also to identify the
interphalangeal joint space without recourse to new US hardware or a new
measurement. We test the approach on phantoms and on a healthy human finger
Passive element enriched photoacoustic computed tomography (PER PACT) for simultaneous imaging of acoustic propagation properties and light absorption\ud
We present a ‘hybrid’ imaging approach which can image both light absorption properties and acoustic transmission properties of an object in a two-dimensional slice using a computed tomography (CT) photoacoustic imager. The ultrasound transmission measurement method uses a strong optical absorber of small cross-section placed in the path of the light illuminating the sample. This absorber, which we call a passive element acts as a source of ultrasound. The interaction of ultrasound with the sample can be measured in transmission, using the same ultrasound detector used for photoacoustics. Such measurements are made at various angles around the sample in a CT approach. Images of the ultrasound propagation parameters, attenuation and speed of sound, can be reconstructed by inversion of a measurement model. We validate the method on specially designed phantoms and biological specimens. The obtained images are quantitative in terms of the shape, size, location, and acoustic properties of the examined heterogeneitie
Sparse approximations of protein structure from noisy random projections
Single-particle electron microscopy is a modern technique that biophysicists
employ to learn the structure of proteins. It yields data that consist of noisy
random projections of the protein structure in random directions, with the
added complication that the projection angles cannot be observed. In order to
reconstruct a three-dimensional model, the projection directions need to be
estimated by use of an ad-hoc starting estimate of the unknown particle. In
this paper we propose a methodology that does not rely on knowledge of the
projection angles, to construct an objective data-dependent low-resolution
approximation of the unknown structure that can serve as such a starting
estimate. The approach assumes that the protein admits a suitable sparse
representation, and employs discrete -regularization (LASSO) as well as
notions from shape theory to tackle the peculiar challenges involved in the
associated inverse problem. We illustrate the approach by application to the
reconstruction of an E. coli protein component called the Klenow fragment.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS479 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Sampling functions for multimode homodyne tomography with a single local oscillator
We derive various sampling functions for multimode homodyne tomography with a
single local oscillator. These functions allow us to sample multimode
s-parametrized quasidistributions, density matrix elements in Fock basis, and
s-ordered moments of arbitrary order directly from the measured quadrature
statistics. The inevitable experimental losses can be compensated by proper
modification of the sampling functions. Results of Monte Carlo simulations for
squeezed three-mode state are reported and the feasibility of reconstruction of
the three-mode Q-function and s-ordered moments from 10^7 sampled data is
demonstrated.Comment: 12 pages, 8 figures, REVTeX, submitted Phys. Rev.
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