Systems and methods for adaptive probing of piecewise continuous surfaces

A method for reconstructing an image of a sample, the method comprising:

• receiving first data corresponding to a plurality of probe points of the sample;
• generating a first estimate of a piecewise continuous surface based on the first data;
• and
• using a machine learning algorithm to perform adaptive probing on the piecewise continuous surface to obtain a reconstructed image of the sample.

A system for reconstructing an image of a sample, the system comprising:

• a processor;
• a display in operable communication with the processor;
• and
• a machine-readable medium in operable communication with the processor and the display and having instructions thereon that, when executed, perform the following steps:
• receiving first data corresponding to a plurality of probe points of the sample;
• generating a first estimate of a piecewise continuous surface based on the first data;
• using a machine learning algorithm to perform adaptive probing on the piecewise continuous surface to obtain a reconstructed image of the sample;
• and
• displaying the reconstructed image of the sample on the display,
• wherein the using of the machine learning algorithm to perform adaptive probing on the piecewise continuous surface comprises:
• i) identifying, by the machine learning algorithm based on the first estimate of the piecewise continuous surface, an updated plurality of probe points of the sample;
• ii) receiving, by the machine learning algorithm, updated data corresponding to the updated plurality of probe points of the sample;
• iii) generating, by the machine learning algorithm, an updated estimate of the piecewise continuous surface based on the updated data;
• iv) identifying, by the machine learning algorithm based on the updated estimate of the piecewise continuous surface, an updated plurality of probe points of the sample;
• and
• v) iteratively repeating substeps ii)-iv) until the updated data is sufficient data to generate an accurate reconstructed image,
• wherein in substeps i) and iv), the updated plurality of probe points of the sample are identified using a jump Gaussian process (JGP), and
• wherein the JGP uses mean square prediction error (MSPE).