Abstract: Systems and methods for reconstruction of missing data using iterated geometric harmonics are described herein. A method includes receiving a dataset having missing entries, initializing missing values in the dataset with random data, and then performing the following actions for multiple iterations. The iterated actions include selecting a column to be updated, removing the selected column from the dataset, converting the dataset into a Gram matrix using a kernel function, extracting rows from the Gram matrix for which the selected column does not contain temporary values to form a reduced Gram matrix, diagonalizing the reduced Gram matrix to find eigenvalues and eigenvectors, constructing geometric harmonics using the eigenvectors to fill in missing values in the dataset, and filling in missing values to improve the dataset and create a reconstructed dataset. The result is a reconstructed dataset. The method is particularly useful in reconstructing image and video files.

Abstract: Systems and methods for reconstruction of missing data using iterated geometric harmonics are described herein. A method includes receiving a dataset having missing entries, initializing missing values in the dataset with random data, and then performing the following actions for multiple iterations. The iterated actions include selecting a column to be updated, removing the selected column from the dataset, converting the dataset into a Gram matrix using a kernel function, extracting rows from the Gram matrix for which the selected column does not contain temporary values to form a reduced Gram matrix, diagonalizing the reduced Gram matrix to find eigenvalues and eigenvectors, constructing geometric harmonics using the eigenvectors to fill in missing values in the dataset, and filling in missing values to improve the dataset and create a reconstructed dataset. The result is a reconstructed dataset. The method is particularly useful in reconstructing image and video files.