Compressed sensing allows for the acquisition of compressible signals with a small number of measurements. In experimental settings, the sensing process corresponding to the hardware implementation is not always perfectly known and may require a calibration. To this end, blind calibration proposes to perform at the same time the calibration and the compressed sensing. Schülke and collaborators suggested an approach based on approximate message passing for blind calibration (cal-AMP) in (Schülke C et al 2013 Advances in Neural Information Processing Systems 26 1–9 and Schülke C et al 2015 J. Stat. Mech. P11013). Here, their algorithm is extended from the already proposed offline case to the online case, for which the calibration is refined step by step as new measured samples are received. We show that the performance of both the offline and the online algorithms can be theoretically studied via the state evolution formalism. Finally, the...

中文翻译：

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压缩传感的盲校准：状态演化和在线算法

压缩感测允许通过少量测量来获取可压缩信号。在实验设置中，与硬件实现相对应的感测过程并不总是完全已知的，可能需要进行校准。为此，盲校准建议同时执行校准和压缩感测。Schülke和合作者在（SchülkeC等人2013年神经信息处理系统的进展26 1–9和SchülkeC等人2015 J. Stat。Mech。P11013）中提出了一种基于近似消息传递的盲校准（cal-AMP）方法。 。在这里，他们的算法从已经提出的离线案例扩展到在线案例，当接收到新的测量样本时，逐步完善校准。我们表明，离线和在线算法的性能都可以通过状态演化形式主义从理论上进行研究。最后，...