Performance evaluation of popular l1-minimization algorithms in the context of Compressed Sensing

Compressed sensing (CS) is a data acquisition technique that is gaining popularity because of the fact that the reconstruction of the original signal is possible even if it was sampled at a sub-Nyquist rate. In contrast to the traditional sampling method, in CS we take a few measurements from the signal and the original signal can then be reconstructed from these measurements by using an optimization technique called l1-minimization. Computer engineers and mathematician have been equally fascinated by this latest trend in digital signal processing. In this work we perform an evaluation of different l1-minimization algorithms for their performance in reconstructing the signal in the context of CS. The algorithms that have been evaluated are PALM (Primal Augmented Lagrangian Multiplier method), DALM (Dual Augmented Lagrangian Multiplier method) and ISTA (Iterative Soft Thresholding Algorithm). The evaluation is done based on three parameters which are execution time, PSNR and RMSE.