A fast scanning ion conductance microscopy imaging method using compressive sensing and low-discrepancy sequences

A scanning ion conductance microscope (SICM) is a multifunctional, high-resolution imaging technique whose non-contact nature makes it very suitable for imaging of biological samples such as living cells in a physiological environment. However, a drawback of hopping/backstep mode of SICM is its relatively slow imaging speed, which seriously restricts the study on the dynamic process of biological samples. This paper presents a new undersampled scanning method based on Compressed Sensing (CS-based scanning mode) theory to solve extended acquisition time issues in the hopping/backstep mode. Compressive sensing can break through the limit of the Nyquist sampling theorem and sample the original sparse/compressible signal at a rate lower than the Nyquist frequency. In the CS-based scanning mode, three sampling patterns, including the random sampling pattern and two kinds of sampling patterns produced by low-discrepancy sequences, were employed as the measurement locations to obtain the undersampled data with different undersampling ratios. Also TVAL3 (Total Variation Augmented Lagrangian ALternating-direction ALgorithm) was then utilized as a reconstruction algorithm to reconstruct the undersampled data. Compared with the nonuniform sampling points of random patterns at a low undersampling ratio, low-discrepancy sequences can produce a more uniform distribution point. Three types of samples with different complexity of topography were scanned by SICM using the conventional hopping/backstep mode and CS-based undersampled scanning mode. The comparisons of the imaging speed and quality with two scanning modes illustrate that the CS-based scanning mode can effectively speed up SICM imaging speed while not sacrificing the image quality. Also low-discrepancy sampling patterns can achieve a better reconstruction performance than that of the random sampling pattern under the same undersampling ratio.