166,051 research outputs found
Proof of Convergence and Performance Analysis for Sparse Recovery via Zero-point Attracting Projection
A recursive algorithm named Zero-point Attracting Projection (ZAP) is
proposed recently for sparse signal reconstruction. Compared with the reference
algorithms, ZAP demonstrates rather good performance in recovery precision and
robustness. However, any theoretical analysis about the mentioned algorithm,
even a proof on its convergence, is not available. In this work, a strict proof
on the convergence of ZAP is provided and the condition of convergence is put
forward. Based on the theoretical analysis, it is further proved that ZAP is
non-biased and can approach the sparse solution to any extent, with the proper
choice of step-size. Furthermore, the case of inaccurate measurements in noisy
scenario is also discussed. It is proved that disturbance power linearly
reduces the recovery precision, which is predictable but not preventable. The
reconstruction deviation of -compressible signal is also provided. Finally,
numerical simulations are performed to verify the theoretical analysis.Comment: 29 pages, 6 figure
Partitions of Minimal Length on Manifolds
We study partitions on three dimensional manifolds which minimize the total
geodesic perimeter. We propose a relaxed framework based on a
-convergence result and we show some numerical results. We compare our
results to those already present in the literature in the case of the sphere.
For general surfaces we provide an optimization algorithm on meshes which can
give a good approximation of the optimal cost, starting from the results
obtained using the relaxed formulation
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