Three-dimensional porous structure reconstruction based on structural local similarity via sparse representation on micro-computed-tomography images

Abstract

A tomographic or image representation of three-dimensional (3D) porous media is a primary tool for the consistent correlation and prediction of multiple physical properties. For multiscale media a single imaging scale may not be sufficient, and a compromise between field of view and resolution is required. The resulting lower resolution compared to relevant length scales in part of the tomogram impacts on the quality of petrophysical cross-correlations. This situation is overcome in geostatistics by carrying out stochastic simulations with lower resolution constraints and propagating uncertainty from smaller scales through upscaling procedures capturing the behavior of the system at smaller scales. Applying this technique to full tomograms requires a fast high-resolution reconstruction technique. We propose a local-similarity statistic reconstruction (LSSR) method to reconstruct 3D high-resolution porous structure by combining a set of increasing resolution micro-computed-tomography (micro-CT) images with decreasing field of view (FOV) to overcome this limitation. The reconstruction technique is based on two assumptions, universally existent local similarity at a given scale and fixed image degradation when downscaling by the same factor between corresponding cubes of high- and low-resolution images. Utilizing the flexibility of micro-CT images in terms of resolution and FOV, a sample was scanned first with low resolution, and then a subset was taken from this sample and scanned with high resolution. A significant number of small cube pairs are extracted from corresponding parts of the low-resolution and high-resolution images, where both high- and low-resolution images are accessible. These cube pairs contain abundant information about features of local porous structure under different resolutions allowing reconstruction of a higher-resolution micro-CT image. Instead of the ``Search-Statistic'' strategy popularly used in current reconstruction algorithm a ``Decomposition-Reconstruction'' strategy is applied to accelerate computations and improve the reconstruction accuracy. Local porosity theory and the Minkowski measures are used to estimate the performance of reconstruction algorithms. Compared to multipoint statistics we improve computational efficiency by employing a sparse representation and principal component analysis for compression, while also improving on reconstruction accuracy.