High dimensional transcriptome profiling, whether through next generation sequencing techniques or high-throughput arrays, may result in scattered variables with missing data. Data imputation is a common strategy to maximize the inclusion of samples by using statistical techniques to fill in missing values. However, many data imputation methods are cumbersome and risk introduction of systematic bias. Here we present a new data imputation method using constrained least squares and algorithms from the inverse problems literature and present applications for this technique in miRNA expression analysis. The proposed technique is shown to offer an imputation orders of magnitude faster, with greater than or equal accuracy when compared to similar methods from the literature.