The problem of reconstructing the magnitude of a complex-valued imagefromincomplete phase data of its Fourier transform is investigated. This is done by formulating the problem as passing the image through a bandpas...
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ISBN:
(纸本)0879426004
The problem of reconstructing the magnitude of a complex-valued imagefromincomplete phase data of its Fourier transform is investigated. This is done by formulating the problem as passing the image through a bandpass filter of bandwidth Δ corresponding to the data sample size and evaluating the magnitude of the resulting image. It is revealed that the reconstruction is essentially equivalent to the magnitude of the resulting image obtained by passing the original magnitude function through a set of two-dimensional extended all-pass filters. The concept of an extended all-pass filter is introduced to describe a filter whose amplitude response spreads over the whole frequency space with random variations. It is shown that the quality of the reconstruction is content-dependent and improves with increase of the sample size.
Modern high sensitivity radio interferometric telescopes use ultra wide-band receivers on a large number of antenna elements to achieve the capability of imaging dynamic ranges in excess of 1:1,000,000. In practice, t...
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ISBN:
(纸本)9780819492173
Modern high sensitivity radio interferometric telescopes use ultra wide-band receivers on a large number of antenna elements to achieve the capability of imaging dynamic ranges in excess of 1:1,000,000. In practice, the imaging performance is limited by instrumental and ionospheric/atmospheric effects that corrupt the recorded data. Many of these effects are directionally dependent and vary with time and frequency. Correcting for them is therefore fundamentally more difficult and these effects have been ignored in classical imagereconstruction algorithms. Few attempts in the past to correct for these effects in the image-domain did not deliver the required accuracy. Recent developments in new algorithms that can account for such direction dependent effects show promising results. In this paper I give a general mathematical description of these techniques, show that the resulting algorithms are more optimal in terms of imaging performance and computing requirements and show some results.
The central problem in the determination of protein structures from x-ray diffraction data (x-ray crystallography) corresponds to a phase retrieval problem with undersampled amplitude data. Algorithms for this problem...
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ISBN:
(纸本)0819437689
The central problem in the determination of protein structures from x-ray diffraction data (x-ray crystallography) corresponds to a phase retrieval problem with undersampled amplitude data. Algorithms for this problem that have an increased radius of convergence have the potential for reducing the amount of experimental work, and cost, involved in determining protein structures. We describe such an algorithm. Application of the algorithm to a simulated crystallographic problem shows that it converges to the correct solution, with no initial phase information, where currently used algorithms fail. The results lend support to the possibility of ab initio phasing in protein crystallography.
Many significant features of images are represented in their Fourier transform. The spectral phase of an image can often be measured more precisely than magnitude for frequencies of up to a few GHz. However, spectral ...
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ISBN:
(纸本)0819445592
Many significant features of images are represented in their Fourier transform. The spectral phase of an image can often be measured more precisely than magnitude for frequencies of up to a few GHz. However, spectral magnitude is the only measurable data in many imaging applications. In this paper, the reconstruction of complex-valued images from either the phases or magnitudes of their Fourier transform is addressed. Conditions for unique representation of a complex-valued image by its spectral magnitude combined with additional spatial information is investigated and presented. reconstruction algorithms of complex-valued images are developed and introduced. Three types of reconstruction algorithms are presented. (1) Algorithms that reconstruct a complex-valued imagefrom the magnitude of its discrete Fourier transform and part of its spatial samples based on the autocorrelation function. (2) Iterative algorithms based on the Gerchberg and Saxton approach. (3) Algorithms that reconstruct a complex-valued imagefrom its localized Fourier transform magnitude. The advantages of the proposed algorithms over the presently available approaches are presented and discussed.
The proceedings contains 22 papers from the SPIE conference on imagereconstructionfromincompletedata II. Topics discussed include: comparison of reconstruction algorithms for images from sparse-aperture systems;im...
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The proceedings contains 22 papers from the SPIE conference on imagereconstructionfromincompletedata II. Topics discussed include: comparison of reconstruction algorithms for images from sparse-aperture systems;imaging fluorescence parameters by Bayesian optical diffusion tomography;blind deconvolution of speckle images constrained by wavefront sensing data;automated target morphing applied to objects in cluttered backgrounds;reconstruction of seismic data using adaptive regularization;and continuous and discrete space particle filters for predictions in acoustic positioning.
Accurate reconstruction of attenuation maps fromincomplete sinograms are required in some cases of SPECT and PET imaging. This paper proposes a new method to directly reconstruct segmented attenuation maps from the i...
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Accurate reconstruction of attenuation maps fromincomplete sinograms are required in some cases of SPECT and PET imaging. This paper proposes a new method to directly reconstruct segmented attenuation maps from the incomplete sinograms. The proposed method is based on an image labeling technique where an optimum label configuration minimizing some energy function is found by using a stochastic sampling with simulated annealing Unlike ordinary image labeling techniques, however, we introduce a powerful constraint called the topology-preserving constraint. This constraint reduces the search space to a set of label configurations having the same topology as the known topology of the attenuation map in question. The experimental results demonstrate that the topology-preserving constraint is powerful enough to reconstruct accurate segmented attenuation aiaps from the incomplete sinograms. The proposed method is tested with simulated data and PET transmission data.
Sparsity of the TSAR images is exploited with the aim to use the possibility of applying an under-sampling strategy as assumed by the compressive sensing approach. The signal sparsity is a desirable property that need...
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ISBN:
(纸本)9781509022212
Sparsity of the TSAR images is exploited with the aim to use the possibility of applying an under-sampling strategy as assumed by the compressive sensing approach. The signal sparsity is a desirable property that needs to be satisfied in order to reconstruct the signals and images from the compressive sensed data. It is assumed that certain amount of radar data is not available and the idea is to reconstruct the radar imagefrom the rest of the data. The signal samples are observed in the spatial domain, and the reconstruction is based on the total variation minimization. The procedure is tested on both, synthetic and real TSAR image, showing satisfactory reconstruction quality with a small set of acquired samples.
In seismic data processing, we often need to interpolate/extrapolate missing spatial locations in a domain of interest. The reconstruction problem can be posed as an inverse problem where from inadequate and incomplet...
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ISBN:
(纸本)0819445592
In seismic data processing, we often need to interpolate/extrapolate missing spatial locations in a domain of interest. The reconstruction problem can be posed as an inverse problem where from inadequate and incompletedata one attempts to recover the complete band-limited seismic wavefield. However, the problem is often ill posed due to factors such as inaccurate knowledge of bandwidth and noise. In this case, regularization can be used to help to obtain a unique and stable solution. In this paper, we formulate band-limited datareconstruction as a minimum norm least squares type problem where an adaptive DFT-weighted norm regularization term is used to constrain the solution. In particular, the regularization term is iteratively updated through using the modified periodogram of the estimated data. The technique allows for adaptive incorporation of prior knowledge of the data such as the spectrum support and the shape of the spectrum. The adaptive regularization can be accelerated using FFTs and an iterative solver like preconditioned conjugate gradient algorithm. Examples on synthetic and real seismic data illustrate improvement of the new method over damped least squares estimation.
Airflow over mountainous terrain can produce stationary atmospheric waves in the lee of the mountains that have large vertical air velocities. These waves are used as sources of lift by sailplane pilots. Methods are d...
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ISBN:
(纸本)0819455008
Airflow over mountainous terrain can produce stationary atmospheric waves in the lee of the mountains that have large vertical air velocities. These waves are used as sources of lift by sailplane pilots. Methods are developed for inverting flight data of airspeed and GPS-derived position to obtain estimates of the vector windspeed in mountain waves. datafrom flight path segments with significantly different ground velocities within a region of constant windspeed give a well-determined solution for the windspeed. The methods are applied to flight datafrom a Perlan Project flight in lee waves of the Sierra Nevada Mountains in California.
The optical instrument function is used as the basis to develop optical system theory for imaging applications. The detection of optical signals is conveniently described as the overlap integral of the Wigner distribu...
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ISBN:
(纸本)9781628417661
The optical instrument function is used as the basis to develop optical system theory for imaging applications. The detection of optical signals is conveniently described as the overlap integral of the Wigner distribution functions of instrument and optical signal. Based on this framework various optical imaging systems, including plenoptic cameras, phase-retrieval algorithms, and Shack-Hartman sensors are shown to acquire information about a domain in phase-space, with finite extension and finite resolution. It is demonstrated how phase space optics can be used both to analyze imaging systems, as well as for designing methods for imagereconstruction.
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