An efficient recovery algorithms using complex to real transformation of compressed sensing

摘要

Compressed sensing is an important topic in signal processing that provides the reconstruction of a signal from a small number of linear measurements. The condition for compressed sensing is that the input signal must be sparse. Some signals are sparse in time domain and other signals must be converted to the frequency domain to be sparse. In this paper, sparse signal in the frequency domain will be assumed. When the signal is converted to sparse by using transform domain, it will cause the complex representation of both the sensing matrix and the input signal. To overcome this complexity, an efficient complex to real transformation technique is proposed to enhance the system performance. Furthermore, the sparse signal is recovered in less time and minimum error. Also, the signal to error ratio from the recovery process is increased. The proposed algorithm removes the imaginary parts and doubles the size of both the sensing matrix and the sparse signal by separating the real and complex variables to remove complexity.