The gappy POD is a is a modification of the basic POD method that handles incomplete or “ gappy ” data sets. An incomplete data vector can be reconstructed by representing it as a linear combination of known POD basis vectors. The modal content is determined by solving a small linear system. Further, if the snapshots themselves are damaged or incomplete, an iterative method can be used to derive the POD basis vectors. This method was developed by Everson and Sirovich in the context of reconstruction of images, such as human faces, from partial data.
The gappy POD is relevant for flow problems where incomplete data is available. For example, in experiments, data may only be available on the airfoil surface. Our research has shown that the gappy POD can be used to reconstruct both steady and unsteady flowfield data from limited surface pressure measurements.