发表机构
Iran University of Science and Technology（伊朗理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究未知复增益下压缩单频估计的奇异速率与全局可识别性，分析局部信息保留、奇异可恢复性和全局可识别性的不同压缩规律，推导了相关均方误差速率、最优解及信息代价等关键结论。
AI 中文摘要
固定线性压缩可保留正弦信号的局部Fisher信息，但会破坏全局频率识别；而暗响应会使局部估计非正则。本文研究了在未知非零复增益和预 sketch 白高斯噪声下，通过固定复线性 sketch 观测到的单个复 tone 的这两种失效情况。在孤立解析暗频率附近，我们将径向信号消失与两个带符号频率分支之间的优化投影接触分离开来。当增益幅度被约束在固定非退化区间时，有限接触等价于局部商可识别性和极小极大一致性。尖锐均方误差速率由径向阶数和接触阶数之和决定；无限接触会产生精确的局部别名。在全局层面，我们在白化行空间上构建了最坏频率有效信息目标，对每个偶数输出秩精确求解该目标，证明了对称边缘投影器的唯一性和定量刚性，并求解了偶数孔径共秩一的情况。秩二的最优解是别名的，且缠绕障碍为全局识别的信息代价提供了正下界；从三个输出开始，具有沉浸式投影响应的全局可识别 sketch 是开集且稠密的，在上确界层面代价为零，对于每个至少为四的偶数秩，精确优化器都具有该性质。因此，在同一估计模型内，局部信息保留、奇异可恢复性和全局可识别性遵循不同的压缩规律。
英文摘要
Fixed linear compression can preserve local Fisher information for a sinusoid yet destroy global frequency identification, while a dark response can make local estimation nonregular. We study both failures for a single complex tone observed through a fixed complex-linear sketch with unknown nonzero complex gain and pre-sketch white Gaussian noise. Near an isolated analytic dark frequency, we separate radial signal vanishing from optimized projective contact between the two signed frequency branches. When the gain magnitude is constrained to a fixed nondegenerate interval, finite contact is equivalent to local quotient identifiability and minimax consistency. The sharp mean-square-error rate is determined by the sum of the radial and contact orders; infinite contact produces exact local aliases. Globally, we formulate a worst-frequency efficientinformation objective on whitened row spaces. We solve it exactly for every even output rank, prove uniqueness and quantitative rigidity of the symmetric-edge projector, and solve the evenaperture co-rank-one case. The rank-two optimum is aliased, and a winding obstruction gives a positive lower bound on the information price of global identification. From three outputs onward, sketches that are globally identifying with an immersive projective response are open and dense and have zero price at the level of suprema; for every even rank of at least four, the exact optimizer has this property. Thus local information preservation, singular recoverability, and global identifiability obey distinct compression laws within one estimation model.
