Image restoration by the method of generalized projections with application to restoration from magnitude

Levi, Aharon; Stark, Henry

doi:10.1109/icassp.1984.1172785

Cited by 27 publications

(25 citation statements)

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“…The design approach of [8,9] alternates between shaping the PSD of a waveform to achieve a desired spectral window (including both in-band and roll-off spectrum) and shaping the time-domain structure (to be either constant amplitude or low-loss), until convergence is reached. This approach is a specific form of alternating projection optimization [10,11,12].…”

Section: Mimo Joint Spectrum/beampattern Optimizationmentioning

confidence: 99%

“…Inserting this relationship into (11) and dividing the numerator and denominator by the center frequency cent f yields…”

Section: A Initialization Of Optimization Parametersmentioning

confidence: 99%

“…Wideband MIMO beampattern synthesis has also been studied in [6,7]. In the spirit of [7], here a wideband MIMO emission optimization approach is developed that leverages recent work on the spectral shaping optimization of physically realizable FM waveforms [8,9], which is itself a specific manifestation of alternating projections [10,11,12]. In [8,9], the FM waveform power spectral density (PSD) was designed to possess a Gaussian shape, which corresponds to low autocorrelation sidelobes [13].…”

Section: Introductionmentioning

confidence: 99%

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Joint spectrum/beampattern design of wideband FM MIMO radar emissions

McCormick

Blunt

Metcalf

2016

2016 IEEE Radar Conference (RadarConf)

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The co-design of multiple-input multiple-output (MIMO) radar waveforms and the associated beampattern is desirable to maximize transmitted power in directions of interest while still maintaining acceptable waveform correlation properties. While MIMO is an emerging technology in radar, one must also consider the stringent spectral requirements that are currently being imposed now and that may become even more stringent in the future. In this paper a MIMO optimization method based on alternating projections is introduced that optimizes, for a uniform linear array, the constant-modulus, continuous-time, element-level waveforms to produce a spectral shape in various desired spatial directions denoted "beams of interest". The resulting beampattern is directly related to these chosen "beams of interest". To address the physical nature of the MIMO emission, the energy stored in the invisible space (i.e. not radiated into the far-field) is considered. It is shown that this stored energy, which could damage the transmitter if operated at high power, can effectively be minimized by optimizing the beampattern based on the visible emission space.

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Section: Mimo Joint Spectrum/beampattern Optimizationmentioning

confidence: 99%

“…Inserting this relationship into (11) and dividing the numerator and denominator by the center frequency cent f yields…”

Section: A Initialization Of Optimization Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Joint spectrum/beampattern design of wideband FM MIMO radar emissions

McCormick

Blunt

Metcalf

2016

2016 IEEE Radar Conference (RadarConf)

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“…A general iterative approach for phase retrieval algorithms was first presented by Gerchberg and Saxton [4] and then further developed by other researchers [8, 9]. Now it has evolved into a large bunch of related iterative algorithms with a broad spectrum of applications in electron microscopy, wave front sensing, astronomy, crystallography and many other fields.…”

Section: Theories and Algorithmsmentioning

confidence: 99%

A comparison of iterative algorithms and a mixed approach for in-line X-ray phase retrieval

Meng¹,

Zhang²,

Wu³

et al. 2009

Optics Communications

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Previous studies have shown that iterative in-line x-ray phase retrieval algorithms may have higher precision than direct retrieval algorithms. This communication compares three iterative phase retrieval algorithms in terms of accuracy and efficiency using computer simulations. We found the Fourier transformation based algorithm (FT) is of the fastest convergence, while the Poisson-solver based algorithm (PS) has higher precision. The traditional Gerchberg-Saxton algorithm (GS) is very slow and sometimes does not converge in our tests. Then a mixed FT-PS algorithm is presented to achieve both high efficiency and high accuracy. The mixed algorithm is tested using simulated images with different noise level and experimentally obtained images of a piece of chicken breast muscle. KeywordsPhase retrieval; X-ray phase imaging; Phase contrast BackgroundIn the booming field of in-line phase-sensitive x-ray imaging, there are two closely related techniques: phase contrast imaging and phase retrieval [1]. The former is a imaging modality that aims to enhance the total contrast of the images using the differential phase shift induced by the object under investigation. By presenting much higher visibility of details inside soft tissues than the traditional attenuation based imaging, it is promising to be a valuable diagnostic tool for applications like mammography. The latter is basically a mathematical technique of solving the diffraction integral, which describes the formation of the phase contrast images, Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers

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“…Recently, a method has been reported which is based on a sequence of intensity measurements of the subjected wave field throughout a volume [4,5]. In order to recover the phase, an iterative process [6] based on the method of generalized projections [7] is employed. In order to recover the phase, an iterative process [6] based on the method of generalized projections [7] is employed.…”

Section: Introductionmentioning

confidence: 99%

Design of an Optical System for Phase Retrieval based on a Spatial Light Modulator

Falldorf¹,

Agour²,

Kopylow³

et al. 2010

AIP Conference Proceedings

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We present an optical configuration for phase retrieval from a sequence of intensity measurements. The setup is based on a 4f-configuration with a phase modulating spatial light modulator (SLM) located in the Fourier domain. The SLM is used to modulate the incoming light with the transfer function of propagation, thus a sequence of propagated representations of the subjected wave field can be captured across a common sensor plane. The main advantage of this technique is the greatly reduced measurement time, since no mechanical adjustment of the camera sensor is required throughout the measurement process. The treatise is focused on the analysis of the wave field in the sensor domain. From the discussion a set of parameters is derived in order to minimize disturbing effects arising from the discrete nature of the SLM. Finally, the big potential of this approach is demonstrated by means of experimental investigations with regard to wave field sensing.

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Image restoration by the method of generalized projections with application to restoration from magnitude

Cited by 27 publications

References 1 publication

Joint spectrum/beampattern design of wideband FM MIMO radar emissions

Joint spectrum/beampattern design of wideband FM MIMO radar emissions

A comparison of iterative algorithms and a mixed approach for in-line X-ray phase retrieval

Design of an Optical System for Phase Retrieval based on a Spatial Light Modulator

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