Adaptive under-sampling strategy for fast imaging in compressive sensing-based atomic force microscopy

Compressive sensing (CS) can reconstruct the rest information almost without distortion by advanced computational algorithm, which significantly simplifies the process of atomic force microscope (AFM) scanning with high imaging quality. In common CS-AFM, the partial measurements randomly come from the whole region to be measured, which easily leads to detail loss and poor image quality in regions of interest (ROIs). Consequently, important microscopic phenomena are missed probably. In this paper, we developed an adaptive under-sampling strategy for CS-AFM to optimize the process of sampling. Under a certain under-sampling ratio, the weight coefficient of ROIs and regions of base (ROBs) were set to control the distribution of under-sampling points and corresponding measurement matrix. A series of simulations were completed to demonstrate the relationship between the weight coefficient of ROIs and image quality. After that, we verified the effectiveness of the method on our homemade AFM. Through a lot of simulations and experiments, we demonstrated how the proposed method optimized the sampling process of CS-AFM, which speeded up the process of AFM imaging with high quality.