An Enhanced Subsampling Technique in Compressive Sensing using Linear Interpolation and Random Measurement Matrix

Abstract

In Compressive Sensing, the incoherence of a measurement matrix during subsampling is a crucial requirement for the accurate reconstruction of a signal. However, such incoherence is only probable and not assured when subsampling is done with the widely used random measurement matrix. The study proposes an enhanced subsampling technique that integrates linear interpolation with the conventional random measurement matrix to provide assured incoherence during subsampling in Compressive Sensing. The experiments show that the proposed technique is less costly computationally and does a faster subsampling of an audio digital signal than when the traditional random measurement matrix is used solely. Additionally, the results demonstrated that the proposed technique outperformed state-of-the-art techniques with respect to the accuracy and speed of the signal reconstruction along with the L1 optimization. This was proven through the use of performance evaluation metrics such as computational complexity, execution time and Mean Square Error.