A comparison of data imputation methods using Bayesian compressive sensing and Empirical Mode Decomposition for environmental temperature data

We present two Bayesian compressive sensing (BCS) imputation methods, BCS-on-Signal and BCS-on-IMF, and compare to temporal and spatio-temporal methods. We build sparse BCS models using available data, then use this sparse model for imputation. Most BCS applications have the sparse data distributed across the computational space, in our adaptation the sparse data are outside the reconstruction space. We used 30 years of temperature data and created gaps of 1% (110 days), 5% (1.5 years), 10% (3 years), and 20% (6 years). Performance was not sensitive to gap size with RMSE slightly above 6C for the BCS-on-Signal and Temporal models, the two best methods. The methods which only required data from the target station performed as well as, or better than, the spatio-temporal model which requires data from surrounding stations. Visually the BCS-on-IMF results seem to better represent longer-period random temporal fluctuations while having poorer performance metrics. Display Omitted Evaluated 4 models for imputation of cyclic environmental data.Sparsity-based methods, such as Bayesian Compressive Sensing (BCS) are applicable for data imputation.BCS using only data from the target station performed as well as models requiring data from nearby stations.Goodness-of-fit metrics were similar for gap sizes from 1 to 6 years.There was no best model, however one BCS model was 1st or 2nd in all cases; another had the most visually realistic results.