Learning-based super-dimension (SD) reconstruction of porous media from a single two-dimensional image

The three-dimensional (3D) microscopic pore structure of Reservoir rock directly affects its seepage characteristics and physical properties. A 3D microscopic pore structure can be reconstructed from a single two-dimensional (2D) training image (TI) by using mathematical modeling methods. In this paper, we introduce the concepts of blocks, dictionary and learning into the reconstruction of 3D porous media from the area of example-based super-resolution (SR) reconstruction, and put forward the concept of super-dimension (SD) reconstruction: study the corresponding relations between 2D images and 3D images of real microscopic pore structure of reservoir rock, and use these relations as guidance for the reconstructions of a new 2D image. According to the concept of SD reconstruction, we put forward a new learning-based super-dimension (LBSD) reconstruction algorithm whose basic steps are as follows: (1) Select the training set; (2) build the dictionary; (3) reconstruction. Based on these steps, we did experiments on reconstruction of porous media from a single two-dimensional image. Comprehensive tests show that the reconstructed 3D structure consists with the 3D Micro-CT core sample where the 2D TI is selected from both in morphological characteristics and Statistical characteristics.