Comparison of Classical Interpolation Methods and Compressive Sensing for Missing Data Reconstruction

The emerging of a new compression technique called compressive sensing (CS) has opened various research possibility in many fields. Practically, CS consists of two main steps, which are compression step and reconstruction step. In many cases, the compression step occurs naturally, for example when several data is missing from the complete set of data. Reconstructing for complete data from incomplete data is the original aims of CS reconstruction process. It is therefore also a logical implication of CS as data interpolation method. Given this situation, a research of CS capability for data interpolation is not yet available. In this paper we investigate the capability of CS for data interpolation. Two popular CS reconstruction tools are used: orthogonal matching pursuit (OMP) and convex programming (CVX). We compared these CS reconstruction performance to the standard interpolation methods which are the linear interpolation and spline interpolation. Simulation results show that classical interpolation methods have better performance in term of general accuracy, while CS reconstruction method has advantage on accuracy in reconstructing data that has sharp changes.