Weighted Fidelity in Non-Uniformly Quantized Compressed Sensing

Laurent Jacques (1) , David K. Hammond (2) , Jalal M. Fadili (3)

1 ICTEAM - Institute of Information and Communication Technologies, Electronics and Applied Mathematics
2 Neuroinformatics Center
3 Equipe Image - Laboratoire GREYC - UMR6072

Following the Compressed Sensing (CS) paradigm, this paper studies the problem of recovering sparse or compressible signals from (scalar) non-uniformly quantized measurements. We show that a simple adaptation of the Basis Pursuit De-Quantizer introduced earlier, that is, a sign sensitive weighting of their lp-norm fidelity constraint, yields good SNR improvements in the signal reconstruction. As a good indication of this improvement origin, we prove theoretically that a similar decoder, using a particular side-position-to-level oracle, displays a reduction of the reconstruction error when both the number of measurements and the moment p of the constraint increase. This follows the oversampling principle underlined in our previous study for uniformly quantized CS, with an additional gain provided by the non-uniform quantization. We conclude this paper by showing the efficiency of the approach on 1-D and 2-D signal examples.

Domaines: Traitement des images [eess.IV]

Laurent Jacques, David K. Hammond, Jalal M. Fadili. Weighted Fidelity in Non-Uniformly Quantized Compressed Sensing. IEEE International Conference on Image Processing (ICIP 2011), Sep 2011, Brussels, Belgium. pp.1921 - 1924, ⟨10.1109/ICIP.2011.6115846⟩. ⟨hal-00808632⟩