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Astract-A set of Fourier descriptors for two-dimensional shapes is defined which is complete in the sense that two objects have the same shape if and only if they have the same set of Fourier descriptors. It also is shown that the moduli of the Fourier coefficients of the parameterizing function of the boundary of an object do not contain enough information… (More)
New methods are described for determining tighter upper bounds on the support of an object, given the support of its autocorrelation. These upper bounds are shown, in a digital experiment, to be useful as object-support constraints used with the iterative transform algorithm for solving the phase-retrieval problem.
This paper presents the methods used to adapt the geometric filtering method for speckle reduction to ultrasound imaging The geometric filtering method is an iterative algorithm for speckle reduction which was first applied to radar images obtained with well controlled axial and lateral resolution. The appearance of speckle in ultrasound images is directly… (More)
The phase-retrieval problem consists of the reconstruction of an object from the modulus of its Fourier transform or, equivalently, from its autocorrelation. This paper describes a number of results relating to the reconstruction of the support of an object from the support of its autocorrelation. Methods for reconstructing the object's support are given… (More)
It is shown that the phase-retrieval problem almost always has a solution unique among functions with disconnected supports satisfying a certain common separation condition.
Questions are raised concerning the uniqueness of solutions to the phase-retrieval problem for functions with dis connected support. A counterexample is presented showing the importance of considering the flipping of infinite proper subsets of nonreal zeros.