INCONSISTENT SIGNAL FEASIBILITY PROBLEMS - LEAST-SQUARES SOLUTIONS IN A PRODUCT SPACE
INCONSISTENT SIGNAL FEASIBILITY PROBLEMS - LEAST-SQUARES SOLUTIONS IN A PRODUCT SPACE
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DOI：
10.1109/78.330356
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发表时间：
1994-11-01
影响因子：
5.4
通讯作者：
COMBETTES, PL
中科院分区：
文献类型：
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作者：
COMBETTES, PL
本文提出了求解不一致凸集理论信号综合问题最小二乘解的并行投影法。在乘积空间中重新表述了寻找使到约束集的距离的平方的加权平均值最小的信号的问题，其中该问题等价于寻找位于特定子空间中且距离原始集合的笛卡尔乘积最小距离的点。在乘积空间中通过交替投影法得到解，这自然导致了在原始空间中的平行投影法。分析了所提方法的收敛特性，并演示了信号合成的应用。
In this paper, we present parallel projection methods to find least-squares solutions to inconsistent convex set theoretic signal synthesis problems. The problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space, where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the Cartesian product of the original sets. A solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space. The convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated.