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A Greedy Blind Calibration Method for Compressed Sensing with Unknown Sensor Gains

A Greedy Blind Calibration Method for Compressed Sensing with Unknown Sensor Gains by

Valerio Cambareri,

Laurent Jacques
The realisation of sensing modalities based on the principles of compressed
sensing is often hindered by discrepancies between the mathematical model of
its sensing operator, which is necessary during signal recovery, and its actual
physical implementation, whose values may differ significantly from the assumed
model. In this paper we tackle the bilinear inverse problem of recovering a
sparse input signal and some unknown, unstructured multiplicative factors
affecting the sensors that capture each compressive measurement. Our
methodology relies on collecting a few snapshots under new draws of the sensing
operator, and applying a greedy algorithm based on projected gradient descent
and the principles of iterative hard thresholding. We explore empirically the
sample complexity requirements of this algorithm by testing the phase
transition of our algorithm, and show in a practically relevant instance of
compressive imaging that the exact solution can be obtained with only a few
snapshots.

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