Recovery of Missing Data via Wavelets Followed by High-Dimensional Modeling

Abstract

In this article missing multi-dimensional data imputation is taken into consideration for unevenly spaced data. The only prerequisite information is intended to be the knowledge that would allow us to guess a matrix called a frame. As an example in image processing an inverse discrete cosine transform matrix would be a suitable frame. The main purpose here is to guess such a sparse frame that can represent complete data vector f. By a sparse representation we mean the majority of components being close to zero. In the present article the data imputation using the expected sparse representation is intended to be done in a wavelet or lifting scheme basis. Finally, the generalization to multivariate case will be discussed.