Graph-based Signal Sampling with Adaptive Subspace Reconstruction for Spatially-irregular Sensor Data

Choosing an appropriate frequency definition and norm is critical in graph signal sampling and reconstruction. Most previous works define frequencies based on the spectral properties of the graph and use the same frequency definition and ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>-norm for optimization for all sampling sets. Our previous work demonstrated that using a sampling-set-dependent norm (and corresponding frequency definition) can address challenges in conventional bandlimited approximations for graph signals, particularly with model mismatches and irregularly distributed data. This work proposes a method for selecting sampling sets tailored to the sampling-set-adaptive GFT-based interpolation. When the graph models the inverse covariance of the data, we show that this adaptive GFT enables tracking bandlimited model mismatch error and its effect in reconstruction, leveraging the spectral folding property, analogous to aliasing error in classical DSP. We propose a sampling set selection algorithm to minimize the worst-case bandlimited model mismatch error. We consider partitioning a set of sensors sampling a continuous spatial process as an application. Our experiments show that sampling and reconstruction using sampling-set-adaptive GFT significantly outperform methods that used fixed GFTs and bandwidth-based criterion.