Some implications of zero sheets for blind deconvolution and phase retrieval

Bates, R. H. T.; Quek, Boon Kiat; Parker, Charles R.

doi:10.1364/josaa.7.000468

Cited by 40 publications

(10 citation statements)

References 23 publications

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“…[15,17,181 zeros of the Fourier transform of the pupil plane image, and then allocates those zeros to either the object or the PSF. [15, 1 7,19-21].…”

Section: Iniroductionmentioning

confidence: 99%

<title>Recovery of images from two-color pupil-plane speckle data using object-plane root matching and pupil-plane error minimization</title>

Holmes

Spivey²,

Smith³

1999

SPIE Proceedings

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Coherent light of one color will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of an object. Further information can be obtained if two colors are used, and if the colors are sufficiently close in wavelength that the interference is also measurable. The two speckle patterns and the interference can be shown to provide the minimum information sufficient to form a band-limited image of the object using a root-matching technique described herein. This root-matching technique is performed in the far-field or object plane. This technique is relatively slow and sensitive to noise, and so is supplemented with a technique that minimizes ror in the pupil plane. A hybrid technique that combines the two approaches is shown to reproduce images effectively with reasonable computation time.

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“…[15,17,181 zeros of the Fourier transform of the pupil plane image, and then allocates those zeros to either the object or the PSF. [15, 1 7,19-21].…”

Section: Iniroductionmentioning

confidence: 99%

<title>Recovery of images from two-color pupil-plane speckle data using object-plane root matching and pupil-plane error minimization</title>

Holmes

Spivey²,

Smith³

1999

SPIE Proceedings

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“…In practice, the presence of noise on the data renders H and I irreducible and one must rely on approximate factorization procedures. As mentioned above, one approach to this involves estimating the location of the real and complex zero locations of the spectra in C. Several authors have considered methods for locating and tracking these zero contours, from which it may be possible to identify the zero sheet associated with F from that associated with G [6,8].…”

Section: Blind Deconvolutionmentioning

confidence: 99%

“…Making use of these analytic properties of spectra has received much attention. A possible approach to solving these problems is that of attempting to locate the zero contour of the spectrum in the four dimensional complex space associated with the two dimensional real data domain, [6,7,8]. For small images, zero contours have been traced in the complex domain with sufficient precision to isolate the zero structure associated with the image's spectrum from that associated with the system transfer function.…”

Section: Introductionmentioning

confidence: 99%

<title>Two-dimensional blind deconvolution from point zero locations</title>

Chen

Fiddy

1994

SPIE Proceedings

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Assuming that two-dimensional bandlimited functions are always non-factorizable, one can use this property to separate the product of two bandlimited functions into its respective factors. The contour in C2 on which each bandlimited function is zero, typically intersects with the real plane at isolated points and the location of these zeros can be used to write a factorizable approximation to the original irreducible complex spectrum. From two differently blurred images, the point zero set from the object's spectrum can be separated from those of the blurring functions by inspection, allowing the object to be reconstructed; examples are given and the importance of this for Fourier phase retrieval is also discussed.

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“…Blind deconvolution problems arise in a variety of contexts, and there is a considerable literature on this subject, e.g., [4], [6], [8], [12]- [16], [21], [23], [25], [28], [29]. Because these references consider a different model from the one considered here, the methods developed therein are not tailored for shotnoise data.…”

Section: Introductionmentioning

confidence: 99%