Advances in Electronics and Electron Physics, Vol. 67 by Peter W. Hawkes (ed.)

By Peter W. Hawkes (ed.)

This quantity includes overview articles masking a huge variety of subject matters in snapshot processing and research. the subjects coated comprise photo research - which has united and harmonized a number of heterogeneous fabric; modern methods to the Fourier remodel; quantity theoretic transforms, that are rather appealing for discrete, finite indications; using the Wigner distribution - which encodes either spatial and spectral info, for photograph filtering; and functions of the concept that of data power. those up to date surveys are meant to supply the reader with entry to the newest leads to the super energetic box of photo technology.

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A = G S ......... I .......... 12. Plots of errors versus numberJ of iterations for the starfield with N = 2. ) . ,they have been normalized for convenience of display). 38 R. H. T. BATES AND D. 13. A. TWO-DIMENSIONAL PHASE PROBLEMS FIG. 13 (continued) 39 40 R H. T. BATES AND D. MNYAMA no sudden, catastrophic deterioration such as usually occurs, for instance, when one attempts extrapolation in the presence of noise. , 1984),does of course greatly enhance the practical significance of Fourier phase retrieval algorithms.

Since the ern,= must be real, each cosine overflow must be appropriately countered. We set the argument of the cosine equal to 0 or R, respectively, whenever the righthand side of these two formulas is greater than 1 or less than - 1. We define the fraction of the cosine overflows to be the number of times the magnitudes of the right-hand sides of Eqs. (45) and (46) exceed unity divided by the total number of invocations of these two formulas. On Fourier transforming the I(u,u) shown in Fig. 14a, zero packing the results so that it exists within B(x,y(4), and Fourier transforming back to visibility space, we obtain samples of the visibility intensity at ordinary and in-between sample points defined in Table I1 with N = 2.

32), we return to Eq. (29), thereby setting up an iterative loop which generates successive versions of $(x, y) and Y (u, v). C) as shown in Figs. 7a and 7b. But note that the starfield image would obviously benefit from more iterations (the black spots in Fig. 7b represent negative parts in the image). E) by oversampling by a factor of 2 (N = 2), as is illustrated in Figs. 7c and 7d. C. C). Note that the constraint on the phase function imposed in Eq. (35) only causes f(x, y), as defined by Eq.

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