A fast image reconstruction method based on Bayesian compressed sensing for the undersampled AFM data with noise

Abstract

Compressed sensing (CS) can be used to obtain a signal through undersampling and reconstruction, which enables the atomic force microscope (AFM) to spatially under-sample the topography information to increase the imaging rate and reduce the amount of probesample interaction. However, the imaging mode of the AFM, which would result in the huge occupation of computing resources including computing time and memory space, makes it inefficient and time-consuming to apply the normal image reconstruction method directly to recover the sample topography from undersampled data. And it is unrealistic to recover a high-solution image by the normal compressed sensing. Here, a novel image reconstruction method based on Bayesian compressing sensing for the undersampled AFM data with noise is proposed to significantly reduce the occupation of computing resources while guaranteeing a high-quality image reconstruction. In the proposed method, the AFM image is regarded as a collection of independent vectors and each vector (a subset of the pixels) is recovered separately. The Bayesian compressed sensing is introduced to provide a better reconstruction performance. The reconstruction experiments demonstrate that the proposed method can significantly reduce the occupation of computing resources while achieving high-quality AFM image reconstruction from the undersampled data with noise. The reconstruction time has been shortened from tens of minutes to less than one minute and the RAM used is reduced to only 1/n 2 of the normal algorithms, which allows the AFM image reconstruction from undersampled data to be easily and conveniently achieved in any personal computer.

Fast Scanning Probe Microscopy via Machine Learning: Non‐Rectangular Scans with Compressed Sensing and Gaussian Process Optimization

“…As such, the broad adoption of non‐rectangular scans [ 34–40 ] necessitates the development of the algorithmic tools that allow conversion of the data stream acquired along the fixed or dynamically adjusted probe path on the classical rectangular grids. It should be noted that most of the non‐rectangular scans were motivated by the need to accelerate the scanning speed and were generally either spiral or Lissajous scans.…”

Reducing molecular simulation time for AFM images based on super-resolution methods

“…Figure 5a with a size of 51 × 51 is used to test the impact of the sampling points on the reconstructed results, as shown in Figure 6 . Generally, an undersampling rate of 0.5 could ensure a better reconstruction effect for BCS [ 47 ]. This image contains 2601 pixels and the undersampling rates of 0.11 (298 pixels), 0.30 (784 pixels), and 0.50 (1300 pixels) are chosen to reconstruct the complete image.…”

“…The CS reconstruction problem is converted into a linear regression problem and the parameter s can be obtained by the maximum likelihood method. The details of the BCS reconstruction algorithm in AFM are given in our previous work [ 47 ].…”

A novel method to remove impulse noise from atomic force microscopy images based on Bayesian compressed sensing

“…The measurement matrix generated by recording the position of the noise-free pixels may not fully meet theoretical reconstruction guarantees. In our previous work [34], which aims to develop a fast AFM image reconstruction from undersampled AFM data, BCS has been proven to be a better method to reconstruct AFM images from undersampled AFM data than other methods. There is also no guarantee that the measurement matrix obtained from the removal of noisy pixels will fully satisfy theoretical reconstruction guarantees.…”

“…The developed reconstruction algorithm can be used to recover the image. The details of the BCS reconstruction algorithm in AFM are given in our previous work [34].…”