According to Nyquist sampling theorem, minimum number of samples for representing a signal without error is dictated by its bandwidth. In recent years a new theory named Compressed Sensing has been raised. This theory focuses on this point that many signals are sparse, so most of their values are zero or around zero. Also many signals can be transformed to another domain (like fourier, DCT, Wavelet and…) to have a sparse representation in that domain. Based on Compressed Sensing and with some special sampling methods, signal can be represented with fewer samples and be reconstructed with that samples. In compressed sensing reconstruction algorithms a sparsity mesure in needed to measure the sparsity of signal. In most of algorithms the L1 norm of signal is used as a sparsity measure. In this thesis using Gini Index as a sparsity measure is checked. Also the results of using Gini Index in Compessed Sensing algorithms are proposed and compared with L1 norm based algorithms. Finally a Compressed Sensing reconstruction algorithm based on Gini Index will be proposed and simulated for some sinals and Images. Keywords: Compressed Sensing, Sparse Signal, Sensing Matrix, Gini Index
