29,177 research outputs found
ON DOUBLE-RESOLUTION IMAGING AND DISCRETE TOMOGRAPHY
Super-resolution imaging aims at improving the resolution of an image by
enhancing it with other images or data that might have been acquired using
different imaging techniques or modalities. In this paper we consider the task
of doubling, in each dimension, the resolution of grayscale images of binary
objects by fusion with double-resolution tomographic data that have been
acquired from two viewing angles. We show that this task is polynomial-time
solvable if the gray levels have been reliably determined. The problem becomes
-hard if the gray levels of some pixels come with an
error of or larger. The -hardness persists for any
larger resolution enhancement factor. This means that noise does not only
affect the quality of a reconstructed image but, less expectedly, also the
algorithmic tractability of the inverse problem itself.Comment: 26 pages, to appear in SIAM Journal on Discrete Mathematic
On the Adjoint Operator in Photoacoustic Tomography
Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from
coupled physics" technique, in which the image contrast is due to optical
absorption, but the information is carried to the surface of the tissue as
ultrasound pulses. Many algorithms and formulae for PAT image reconstruction
have been proposed for the case when a complete data set is available. In many
practical imaging scenarios, however, it is not possible to obtain the full
data, or the data may be sub-sampled for faster data acquisition. In such
cases, image reconstruction algorithms that can incorporate prior knowledge to
ameliorate the loss of data are required. Hence, recently there has been an
increased interest in using variational image reconstruction. A crucial
ingredient for the application of these techniques is the adjoint of the PAT
forward operator, which is described in this article from physical, theoretical
and numerical perspectives. First, a simple mathematical derivation of the
adjoint of the PAT forward operator in the continuous framework is presented.
Then, an efficient numerical implementation of the adjoint using a k-space time
domain wave propagation model is described and illustrated in the context of
variational PAT image reconstruction, on both 2D and 3D examples including
inhomogeneous sound speed. The principal advantage of this analytical adjoint
over an algebraic adjoint (obtained by taking the direct adjoint of the
particular numerical forward scheme used) is that it can be implemented using
currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems
Non-Local Compressive Sensing Based SAR Tomography
Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse
reconstruction problem and, hence, can be solved using compressive sensing (CS)
algorithms. This paper proposes solutions for two notorious problems in this
field: 1) TomoSAR requires a high number of data sets, which makes the
technique expensive. However, it can be shown that the number of acquisitions
and the signal-to-noise ratio (SNR) can be traded off against each other,
because it is asymptotically only the product of the number of acquisitions and
SNR that determines the reconstruction quality. We propose to increase SNR by
integrating non-local estimation into the inversion and show that a reasonable
reconstruction of buildings from only seven interferograms is feasible. 2)
CS-based inversion is computationally expensive and therefore barely suitable
for large-scale applications. We introduce a new fast and accurate algorithm
for solving the non-local L1-L2-minimization problem, central to CS-based
reconstruction algorithms. The applicability of the algorithm is demonstrated
using simulated data and TerraSAR-X high-resolution spotlight images over an
area in Munich, Germany.Comment: 10 page
Neutron imaging and tomography with MCPs
A neutron imaging detector based on neutron-sensitive microchannel plates
(MCPs) was constructed and tested at beamlines of thermal and cold neutrons.
The MCPs are made of a glass mixture containing B-10 and natural Gd, which
makes the bulk of the MCP an efficient neutron converter. Contrary to the
neutron sensitive scintillator screens normally used in neutron imaging,
spatial resolution is not traded off with detection efficiency. While the best
neutron imaging scintillators have a detection efficiency around a percent, a
detection efficiency of around 50% for thermal neutrons and 70% for cold
neutrons has been demonstrated with these MCPs earlier.
Our tests show a performance similar to conventional neutron imaging
detectors, apart from the orders of magnitude better sensitivity. We
demonstrate a spatial resolution better than 150 um. The sensitivity of this
detector allows fast tomography and neutron video recording, and will make
smaller reactor sites and even portable sources suitable for neutron imaging.Comment: Submitted to the proceedings of the 19th International Workshop on
Radiation Imaging Detectors (iWoRiD) 2-6 July 2017, Krakow, Polan
A fast and accurate basis pursuit denoising algorithm with application to super-resolving tomographic SAR
regularization is used for finding sparse solutions to an
underdetermined linear system. As sparse signals are widely expected in remote
sensing, this type of regularization scheme and its extensions have been widely
employed in many remote sensing problems, such as image fusion, target
detection, image super-resolution, and others and have led to promising
results. However, solving such sparse reconstruction problems is
computationally expensive and has limitations in its practical use. In this
paper, we proposed a novel efficient algorithm for solving the complex-valued
regularized least squares problem. Taking the high-dimensional
tomographic synthetic aperture radar (TomoSAR) as a practical example, we
carried out extensive experiments, both with simulation data and real data, to
demonstrate that the proposed approach can retain the accuracy of second order
methods while dramatically speeding up the processing by one or two orders.
Although we have chosen TomoSAR as the example, the proposed method can be
generally applied to any spectral estimation problems.Comment: 11 pages, IEEE Transactions on Geoscience and Remote Sensin
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