Results 1  10
of
252
On Stability of Reconstruction from Fourier Transform Modulus
"... V. CONCLUSION The root structure of median roots is analyzed by applying three different appending strategies. In this correspondence, we have shown that these three appending strategies have a significant effect on the root structure and the cardinality of root set. We also showed that the appended ..."
Abstract
 Add to MetaCart
V. CONCLUSION The root structure of median roots is analyzed by applying three different appending strategies. In this correspondence, we have shown that these three appending strategies have a significant effect on the root structure and the cardinality of root set. We also showed that the appended root signals of the median filter under the circular strategy either consist of constant neighborhoods only or consist of nonconstant neighborhoods only. It is impossible to have a median root under the circular strategy consisting of some constant neighborhoods and some nonconstant neighborhoods.
On the Recovery Of a 2D Function From the Modulus Of Its Fourier Transform
, 2005
"... A uniqueness theorem is proven for the problem of the recovery of a complex valued compactly supported 2D function from the modulus of its Fourier transform. An application to the phase problem in optics is discussed. 1 ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
A uniqueness theorem is proven for the problem of the recovery of a complex valued compactly supported 2D function from the modulus of its Fourier transform. An application to the phase problem in optics is discussed. 1
Hypercomplex fourier transforms of color images
, 2007
"... Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applic ..."
Abstract

Cited by 69 (3 self)
 Add to MetaCart
applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A
Reconstruction of a complexvalued object from the modulus of its Fourier transform using a support constraint
 Journal of Optical Society of America A
, 1987
"... Previously it was shown that one can reconstruct an object from the modulus of its Fourier transform (solve the phaseretrieval problem) by using the iterative Fouriertransform algorithm if one has a nonnegativity constraint and a loose support constraint on the object. In this paper it is shown th ..."
Abstract

Cited by 37 (6 self)
 Add to MetaCart
Previously it was shown that one can reconstruct an object from the modulus of its Fourier transform (solve the phaseretrieval problem) by using the iterative Fouriertransform algorithm if one has a nonnegativity constraint and a loose support constraint on the object. In this paper it is shown
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
Abstract

Cited by 193 (3 self)
 Add to MetaCart
complementary to Fourier preparation by linear field gradients. Thus, by using multiple receiver coils in parallel scan time in Fourier imaging can be considerably reduced. The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil
Fast parallel circuits for the quantum Fourier transform
 PROCEEDINGS 41ST ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS’00)
, 2000
"... We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log(1/ε)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2 n with error bounded by ε. Thus, even for exponentially small error, our ..."
Abstract

Cited by 72 (1 self)
 Add to MetaCart
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log(1/ε)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2 n with error bounded by ε. Thus, even for exponentially small error
Imaging a coherently illuminated object after double passage through a random screen
, 1990
"... We show that the average intensity spectrum for an object illuminated and viewed through the same random screen contains diffractionlimited information on the Fourier modulus of the object amplitude. For physical clarity, the theory is first presented for a twopinhole, Michelson aperture and then ..."
Abstract
 Add to MetaCart
We show that the average intensity spectrum for an object illuminated and viewed through the same random screen contains diffractionlimited information on the Fourier modulus of the object amplitude. For physical clarity, the theory is first presented for a twopinhole, Michelson aperture
On Shor's Quantum Factor Finding Algorithm: Increasing the Probability of Success and Tradeoffs Involving the Fourier Transform Modulus
, 1995
"... It is shown that by combining two runs of Shor's quantum factor finding algorithm, the probability of success can be improved to a constant. The tradeoff between the size of the domain of the Fourier transform and the amount of classical computation is explored. 1 Introduction Shor's quan ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
It is shown that by combining two runs of Shor's quantum factor finding algorithm, the probability of success can be improved to a constant. The tradeoff between the size of the domain of the Fourier transform and the amount of classical computation is explored. 1 Introduction Shor
Reconstruction of a ComplexValued Object from the Modulus of Its Fourier Transform Using a Support Constraint
"... Abstract: It is often possible to reduce the requirements on an imaging system by placing greater demands either on an illumination system or on postdetection processing of the data collected by the system. An extreme example of this is a system with no receiver optics whatsoever. By illuminating ..."
Abstract
 Add to MetaCart
Abstract: It is often possible to reduce the requirements on an imaging system by placing greater demands either on an illumination system or on postdetection processing of the data collected by the system. An extreme example of this is a system with no receiver optics whatsoever. By illuminating an object or scene with coherent light having a shaped illumination pattern, the receiver can be a simple detector array with no imaging optics, detecting the speckle intensity pattern reflected from the object; an image of the object can be reconstructed by a phase retrieval algorithm.
Square Fourier matrix.
"... Abstract—The usual nonparametric approach to spectral analysis is revisited within the regularization framework. Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then, particular attention is paid to their interpretati ..."
Abstract
 Add to MetaCart
Abstract—The usual nonparametric approach to spectral analysis is revisited within the regularization framework. Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then, particular attention is paid
Results 1  10
of
252