Predicting reconstruction quality within compressive sensing for atomic force microscopy

With compressive sensing, the obtainable reconstruction quality depends on the original signal, the reconstruction algorithm, the measurement matrix, and the dictionary matrix. The present paper is concerned with establishing performance indicators and using these to predict reconstruction quality in atomic force microscopy applications. For this purpose, we consider the well-known quantities of coherence and mutual coherence. Furthermore, we propose a new performance indicator derived from coherence in order to better model the average reconstruction quality. Through extensive simulations, affine models using the performance indicators are evaluated in terms of modified coefficients of determination. The results show that the proposed performance indicator yields a better model than both coherence and mutual coherence do. In conclusion, the proposed performance indicator can be used to predict reconstruction quality for the given application, and the affine prediction model can be improved by including coherence and mutual coherence.