Signal reconstruction from one bit of Fourier transform phase

Abstract

In this paper, we present new results on the reconstruction of signals from one bit of Fourier transform phase, defined as th.e sign of the real part of the Fourier transform. Specifically, we develop a new theoretical result which shows that most twodimensioral signals can in fact be reconstructed to within a scale factor from only one bit of FT phase. Experimental results showing images reconstructed from one hit of FT phase are also presented.

Reconstruction of multidimensional signals from zero crossings

“…- 49 -and in [33,34,35] was effectively to map the periodic signal onto the unit surface in the complex space, as opposed to mapping the original signal onto the real plane in complex space as is done in this paper and in [30]. This problem is discussed in more detail in [30].…”

Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

“…Therefore, the iterative blind deconvolution algorithm should not start with the observed image. Image reconstruction from phase (IRP) has been extensively studied by Oppenheim and his coworkers [24]- [27]. IRP problem is a robust inverse problem.…”

“…Image reconstruction from Fourier transform phase information was first considered in 1980's [24]- [27] and total variation based image denoising was introduced in 1990's [28]. However, FT phase information and ESTV have not been used in blind deconvolution problem to the best of our knowledge.…”

Iris recognition by local extremum points of multiscale Taylor expansion

“…The similarity metric defined by (16), (17) and (19), formulas uses fixed angular and radial shifts. In [8], it is shown that iris description based on two circles model is inaccurate and significant improvement of iris recognition can be obtained when an elastic adaptive grid is used for iris pixels positions.…”

“…It is well known that multiscale phase and zero-crossing information is often sufficient for initial signal reconstruction [17,18]. For example 256 × 256 image can be reconstructed [19] from the binarized Fourier transform phase with probability p > 1 − 2 −2000 . Thus, all three iris descriptions with big probability preserve information about the original image texture.…”