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The success of the compressed sensing paradigm has shown that a substantialreduction in sampling and storage complexity can be achieved in certain linearand non-adaptive estimation problems. It is therefore an advisable strategy fornoncoherent information retrieval in, for example, sporadic blind andsemi-blind communication and sampling problems. But, the conventional model isnot practical here since the compressible signals have to be estimated fromsamples taken solely on the output of an un-calibrated system which is unknownduring measurement but often compressible. Conventionally, one has either tooperate at suboptimal sampling rates or the recovery performance substantiallysuffers from the dominance of model mismatch. In this work we discuss such typeof estimation problems and we focus on bilinear inverse problems. We link thisproblem to the recovery of low-rank and sparse matrices and establish stablelow-dimensional embeddings of the uncalibrated receive signals wherebyaddressing also efficient communication-oriented methods like universal randomdemodulation. Exemplary, we investigate in more detail sparse convolutionsserving as a basic communication channel model. In using some recent resultsfrom additive combinatorics we show that such type of signals can beefficiently low-rate sampled by semi-blind methods. Finally, we present afurther application of these results in the field of phase retrieval fromintensity Fourier measurements.

Sparse Model Uncertainties in Compressed Sensing with Application to Convolutions and Sporadic Communication