# “Bilinear Inverse Problems”

### A greedy blind calibration method for compressed sensing with unknown sensor gains

Abstract: 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, which can amply differ from the assumed model.

### A non-convex blind calibration method for randomised sensing strategies

Abstract: The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not require any training, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue.

### Non-Convex Blind Calibration for Compressed Sensing via Iterative Hard Thresholding

Abstract: Real-world applications of compressed sensing are often limited by modelling errors between the sensing operator, which is necessary during signal recovery, and its actual physical implementation. In this paper we tackle the biconvex problem of recovering a sparse input signal jointly with some unknown and unstructured multiplicative factors affecting the sensors that capture each measurement.