压缩感知中未知误差的恢复保证
Recovery guarantees for compressed sensing with unknown errors
AI总结：
本文研究了在无先验噪声估计情况下，l1最小化在有限正交系统中的鲁棒恢复保证，应用于高维函数逼近和磁共振成像等领域。
摘要：
从数值分析角度看，评估l1最小化在压缩感知中的鲁棒性是基础问题。然而，现有文献中的恢复保证通常依赖于先验噪声估计，这在实践中难以获得，尤其当噪声包含有限模型与数据之间的未知差异时。本文研究了在无此类估计情况下l1最小化的表现，为二次约束基 pursuit和有限正交系统的随机采样提供了鲁棒恢复保证。该工作应用于高维函数逼近、无限维稀疏正则化反问题以及非Cartesian磁共振成像的快速算法。
英文摘要：
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori estimates of the noise, which can be very hard to obtain in practice, especially when the noise term also includes unknown discrepancies between the finite model and data. In this work, we study the performance of l1-minimization when these estimates are not available, providing robust recovery guarantees for quadratically constrained basis pursuit and random sampling in bounded orthonormal systems. Several applications of this work are approximation of high-dimensional functions, infinite-dimensional sparse regularization for inverse problems, and fast algorithms for non-Cartesian Magnetic Resonance Imaging.
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