由指定邻近点重构函数
Reconstruction of Functions from Prescribed Proximal Points
摘要：
在研究中的问题是找到希尔伯特空间中的函数的最佳逼近受到凸约束和规定的非线性变换。我们表明，在许多情况下，这些处方可以表示使用坚定的非扩张算子，即使当原来的观察过程是不连续的。因此，所提出的框架捕获了大量的经典和当代最佳逼近问题，如调和分析，统计，插值理论和信号处理等领域。由此产生的问题是重铸方面的一个共同的不动点问题，并解决了一个新的块迭代算法，其特点是近似投影到个人集以及外推松弛计划，利用可能存在的仿射约束。信号恢复的数值应用证明。
英文摘要：
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be represented using firmly nonexpansive operators, even when the original observation process is discontinuous. The proposed framework thus captures a large body of classical and contemporary best approximation problems arising in areas such as harmonic analysis, statistics, interpolation theory, and signal processing. The resulting problem is recast in terms of a common fixed point problem and solved with a new block-iterative algorithm that features approximate projections onto the individual sets as well as an extrapolated relaxation scheme that exploits the possible presence of affine constraints. A numerical application to signal recovery is demonstrated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
