83 research outputs found
A Perfect Match Condition for Point-Set Matching Problems Using the Optimal Mass Transport Approach
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Linear convergence analysis of the use of gradient projection methods on total variation problems
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Matrix balancing based interior point methods for point set matching problems
Full text linkPoint sets matching problems can be handled by optimal transport. The
mechanism behind it is that optimal transport recovers the point-to-point
correspondence associated with the least curl deformation. Optimal transport is
a special form of linear programming with dense constraints. Linear programming
can be handled by interior point methods, provided that the involved
ill-conditioned Hessians can be computed accurately. During the decade, matrix
balancing has been employed to compute optimal transport under entropy
regularization approaches. The solution quality in the interior point method
relies on two ingredients: the accuracy of matrix balancing and the boundedness
of the dual vector. To achieve high accurate matrix balancing, we employ Newton
methods to implement matrix balancing of a sequence of matrices along one
central path. In this work, we apply sparse support constraints to
matrix-balancing based interior point methods, in which the sparse set
fulfilling total support is iteratively updated to truncate the domain of the
transport plan. Total support condition is one crucial condition, which
guarantees the existence of matrix balancing as well as the boundedness of the
dual vector
Blind ptychography: uniqueness and ambiguities
No full textPtychography with an unknown mask and object is analyzed for general ptychographic measurement schemes that are strongly connected and possess an anchor.
Under a mild constraint on the mask phase, it is proved that the masked object estimate must be the product of a block phase factor and the true masked object. This local uniqueness manifests itself in the phase drift equation that determines the ambiguity at different locations connected by ptychographic shifts.The proposed mixing schemes effectively connects the ambiguity throughout the whole domain such that a distinct ambiguity profile arises and consequently possess the global uniqueness that the block phases have an affine profile and that the object and mask can be simultaneously recovered up to a constant scaling factor and an affine phase factor
A Study on the Logistic Service Satisfaction for Internet Marketing Enterprise Using Data Mining Technology
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Fourier Phase Retrieval with a Single Mask by Douglas-Rachford Algorithm
No full textDouglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a
single random phase mask. Local, geometric convergence to a unique fixed point is proved
with numerical demonstration of global convergence
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