5,094 research outputs found
Superposition frames for adaptive time-frequency analysis and fast reconstruction
In this article we introduce a broad family of adaptive, linear
time-frequency representations termed superposition frames, and show that they
admit desirable fast overlap-add reconstruction properties akin to standard
short-time Fourier techniques. This approach stands in contrast to many
adaptive time-frequency representations in the extant literature, which, while
more flexible than standard fixed-resolution approaches, typically fail to
provide efficient reconstruction and often lack the regular structure necessary
for precise frame-theoretic analysis. Our main technical contributions come
through the development of properties which ensure that this construction
provides for a numerically stable, invertible signal representation. Our
primary algorithmic contributions come via the introduction and discussion of
specific signal adaptation criteria in deterministic and stochastic settings,
based respectively on time-frequency concentration and nonstationarity
detection. We conclude with a short speech enhancement example that serves to
highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio
GPU-based Iterative Cone Beam CT Reconstruction Using Tight Frame Regularization
X-ray imaging dose from serial cone-beam CT (CBCT) scans raises a clinical
concern in most image guided radiation therapy procedures. It is the goal of
this paper to develop a fast GPU-based algorithm to reconstruct high quality
CBCT images from undersampled and noisy projection data so as to lower the
imaging dose. For this purpose, we have developed an iterative tight frame (TF)
based CBCT reconstruction algorithm. A condition that a real CBCT image has a
sparse representation under a TF basis is imposed in the iteration process as
regularization to the solution. To speed up the computation, a multi-grid
method is employed. Our GPU implementation has achieved high computational
efficiency and a CBCT image of resolution 512\times512\times70 can be
reconstructed in ~5 min. We have tested our algorithm on a digital NCAT phantom
and a physical Catphan phantom. It is found that our TF-based algorithm is able
to reconstrct CBCT in the context of undersampling and low mAs levels. We have
also quantitatively analyzed the reconstructed CBCT image quality in terms of
modulation-transfer-function and contrast-to-noise ratio under various scanning
conditions. The results confirm the high CBCT image quality obtained from our
TF algorithm. Moreover, our algorithm has also been validated in a real
clinical context using a head-and-neck patient case. Comparisons of the
developed TF algorithm and the current state-of-the-art TV algorithm have also
been made in various cases studied in terms of reconstructed image quality and
computation efficiency.Comment: 24 pages, 8 figures, accepted by Phys. Med. Bio
On the performance of superposition window
Superposition window is often used in the digital signal processing and other fields of signal processing such as power spectral estimation and adaptive time-frequency analysis. Different overlap and windows used in superposition system may affect the final results. The main contribution of this paper is in providing the insight into the properties of the overlap-add technique with different window or overlap ratio, which is very helpful in selecting these parameters for a practical application
Holographic Imaging of Crowded Fields: High Angular Resolution Imaging with Excellent Quality at Very Low Cost
We present a method for speckle holography that is optimised for crowded
fields. Its two key features are an iterativ improvement of the instantaneous
Point Spread Functions (PSFs) extracted from each speckle frame and the
(optional) simultaneous use of multiple reference stars. In this way, high
signal-to-noise and accuracy can be achieved on the PSF for each short
exposure, which results in sensitive, high-Strehl re- constructed images. We
have tested our method with different instruments, on a range of targets, and
from the N- to the I-band. In terms of PSF cosmetics, stability and Strehl
ratio, holographic imaging can be equal, and even superior, to the capabilities
of currently available Adaptive Optics (AO) systems, particularly at short
near-infrared to optical wavelengths. It outperforms lucky imaging because it
makes use of the entire PSF and reduces the need for frame selection, thus
leading to higher Strehl and improved sensitivity. Image reconstruction a
posteriori, the possibility to use multiple reference stars and the fact that
these reference stars can be rather faint means that holographic imaging offers
a simple way to image large, dense stellar fields near the diffraction limit of
large telescopes, similar to, but much less technologically demanding than, the
capabilities of a multi-conjugate adaptive optics system. The method can be
used with a large range of already existing imaging instruments and can also be
combined with AO imaging when the corrected PSF is unstable.Comment: Accepted for publication in MNRAS on 15 Nov 201
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