Analysis and application of compressive sensing technique for rapid magnetic resonance imaging

Shannon/Nyquist sampling theorem states that signal should be sampled at least two times faster than its frequency to avoid any loss in the information, when it is captured. Too high sampling rate results in too many samples. So data compression is required before the signal is stored or transmitted. In some applications such as medical scanners, it is very expensive to increase the sampling rate. An alternative sampling theory known as compressive sensing or compressed sensing (CS) is introduced recently, which facilitates the capturing of a signal or image at a rate considerably below the Nyquist rate. Magnetic resonance imaging (MRI) is an important tool used in medical imaging but has very low data acquisition speed. This makes the patient to be exposed to a scanning machine for a long time. In this work, it is analyzed that how compressive sensing can be applied to MRI without the loss of resolution using number of optimization algorithms and also different optimization algorithms are compared using the parameters such as signal to noise ratio (SNR) and CPU time. This enables the significant reduction in scan time, which benefits both the patient and health care economics.