Mathematics Colloquia and Seminars

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We will discuss a powerful enhancement in performance for phasing with a random mask. We will show that phasing with high resolution random mask and the oversampling ratio 4 determines a unique phasing solution. Under this condition, the simple standard algorithms converge rapidly to the true solution without stagnation. Excellent approximation is achieved after a small number of iterations, not just with high resolution but also low resolution random mask in the presence of additive as well multiplicative noises. Numerics shows that oversampling ratio 2 is sufficient for phasing complex-valued images and ratio 1 for nonnegative images. The error-reduction algorithm with random mask is proved to converge to the true solution under a zero-padding condition.