M.H. Hayes, "The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform," IEEE Trans. ASSP 30(2), 140-154 (1982).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....white Gaussian noise has been treated in the literature. A very simple approach is to use the magnitude of the Fourier transform of the observation as a cyclic shift invariant statistic. However, because this statistic is not maximal, it is invariant to more than just translations. In fact, Hayes [2] has shown for the discrete case that even if the equivalence class includes circular shifts, time reversal, and change of sign of the sequence, the statistic is still not maximal. The result is suboptimality of any detector based on this quantity. A more justifiable approach is to use the ....

Hayes, M. H., "The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-30, pp. 140--154, Apr. 1982.

....white Gaussian noise has been treated in the literature. A very simple approach is to use the magnitude of the Fourier transform of the observation as a cyclic shift invariant statistic. However, because this statistic is not maximal, it is invariant to more than just translations. In fact, Hayes [2] has shown for the discrete case that even if the equivalence class includes circular shifts, time reversal, and change of sign of the sequence, the statistic is still not maximal. The result is suboptimality of any detector based on this quantity. A more justifiable approach is to use the ....

Hayes, M. H., "The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-30, pp. 140--154, Apr. 1982.

....Fax: 972 4 832 3041 Email: mp ee.technion.ac.il 1 1 Introduction It is well known that under certain conditions an image is uniquely represented by its Fourier phase, to within a positive scale factor. Sufficient conditions for unique representation were presented by Oppenheim, Lim and Hayes [1, 2, 3]. Signal representation by partial Fourier phase information has been of interest in several signal processing applications, such as the deconvolution of distorted signals or images affected by a multi path environment [4, 5, 6, 7] The importance of Fourier phase as compared to Fourier magnitude ....

....given in Theorems 2, 3 and the corollary formulated consequently. 8 3. 3 Extension to Two dimensional Signals The uniqueness, to within a positive scale factor, of a multidimensional sequence w = v T ; 0) T , w 2 R 2 N , v(n) 2 R N from its DFT phase has been shown to exist [3] if v has no symmetric factors (4) Images, whose z transform polynomials are of two variables, V (z 1 ; z 2 ) are unlikely to contain symmetric factors [7, 21] Therefore, most images are uniquely represented, to within a positive scale factor, by their DFT phase. The convergence angle ff ....

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M. H. Hayes, "The Reconstruction of a Multidimensional Sequence from the Phase or Magnitude of its Fourier Transform," IEEE Trans. Acoust. Speech, Signal Processing ASSP-30, No. 2, pp. 140-154, April 1982.

....and review some literature on phase retrieval from power spectra of images. Then we present a formal proof that, given the right transform parameters and appropriate band limitation, no image information is lost beside the DC value of the image and a global sign. The proof uses techniques from [10] and applies to all images except a possible subset of measure zero. Finally, we explore the quality of reconstruction by a numerical implementation of the steps in the proof. The results are not perfect because much of the proof depends on transform values being exactly zero, which does not ....

....image properties [19] is frequently interpreted as saying that the Fourier magnitudes contain less image information than the phases. However, analytical results and existing phase retrieval algorithms provide hints that the situation is not as simple. In the following we review two papers [10], 20] which show that, in a certain sense, almost all images can be reconstructed from their Fourier magnitudes. The argument identifies unique reconstructability with the reducibility of a polynomial in D variables, where D is the signal dimension. A. Polynomials in one or more dimensions The ....

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Monson H. Hayes, "The Reconstruction of a Multidimensional Sequence from the Phase or Magnitude of Its Fourier Transform, " IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 30, no. 2, pp. 140 -- 154, April 1982.

....or magnitude is accurately known, and it is desired to reproduce the original signal from this incomplete or distorted spectrum. Such reproduction from the deficient spectrum is referred to as retrieval of the remaining information. A large literature exists on both phase and magnitude retrieval [10,12,14,4,5,7]. In the following section we discuss, without formal argument, how these kinds of results give insight into type images. We give more mathematical detail in a subsequent section. Experimental results In this section we describe the experimental results we have obtained. However, first we want ....

....song10.2250pxl sample: 64 x 64 Figure 4. Reconstruction from phase only CONVERGENCE AND UNIQUENESS We now give the arguments as to why the algorithm described above converges to the original images after finitely many iterations. Discrete Fourier transforms and Z transforms Following Hayes [4] we adopt standard notation for multi dimensional sequences over the real and complex numbers. In what follows, we assume dimension m = 2 if not otherwise stated, but everything holds for greater dimensions. We will observe below that there is a distinction to be made between one dimensional and ....

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Monson H. Hayes, `Reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform', IEEE Transactions on ASSP, 39(2), 140--154 (1982).

....f(n1 ; n2) fi N 1 Gamma1 X k 1 =0 N 2 Gamma1 X k 2 =0 F (k1 ; k2 )e j2k 1 n 1 =N 1 j2k 2 n 2 =N 2 (2) where fi = N1N2) Gamma1=2 . The Discrete Fourier Transform of a real image is generally complex valued. This leads to a magnitude and phase representation for the image. Hayes [12] investigated the relative importance of the magnitude and phase components of the DFT and their effect on the intelligibility of an image. It is demonstrated quite conclusively that the phase is more important than the magnitude of the the DFT values. This is interesting from our point of view ....

M. H. Hayes. The reconstruction of a multidimensional sequence from the phase or magnitude of the FFT. IEEE Trans on Acoustics, Speech and Signal Processing, pages 140--154, April 1992.

.... of residues is common to a series of important physical problems such as wave front reconstruction from turbulence induced phase perturbations [11] coherent imaging [13] phase retrieval from intensity data in optics [14, 15] digital image reconstruction from Fourier transform phase or magnitude [16], speckle interferometry [17] measurement of magnetic field inhomogeneities in magnetic resonance imaging [18, 19, 20, 21] geophysics [22] and generation of high precision digital elevation models (DEM) of a remotely sensed terrain in synthetic aperture radar (SAR) interferometry [23] 3 In ....

M. H. Hayes. The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform. IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP30 (2):140--154, April 1982.

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M.H. Hayes, "The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform," IEEE Trans. ASSP 30(2), 140-154 (1982).

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M..H. Hayes, "The reconstruction of multidimensional sequence from phase or magnitude of its Fourier transform," IEEE Transactions on Acoustics, Speech, and Signal Processing,vol. ASSP-30, pp. 140-154, 1982.

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M. H. HAYES. The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform. IEEETransactions on Acoustics, Speech, and Signal Processing, ASSP30 (2):140--154, April 1982.

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M. H. Hayes, "The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-30, pp. 140--154, 1982.

No context found.

M. Hayes, "The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform", IEEE Trans. ASSP, vol.30, p.140-154, 1982.

No context found.

M.H. Hayes, "The Reconstruction of a Multidimensional Sequence from the Phase or Magnitude of its Fourier Transform", IEEE Trans. on ASSP, vol. 30, No. 2, pp. 140-154, April 1982.

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