Compressed sensing: Doppler ultrasound signal recovery by using non-uniform sampling & random sampling

Several authors have shown that it is possible to reconstruct exactly a sparse signal from a fewer linear measurements, this method known as compressed sensing (CS). CS aim to reconstruct signals and images from significantly fewer measurements. With CS it´s possible to make an accurate reconstruction from small number of samples (measurements). Doppler ultrasound is an important technique for non-invasively detecting and measuring the velocity of moving structure, and particularly blood, within the body. Doppler ultrasound signal has been reconstructed with CS by using random sampling and non-uniform sampling via ℓ1-norm to generate Doppler sonogram. The result show that the recovered signals with non-uniform sampling are the same as the original signal, there is a loss of very small peaks, when random sampling used for recovering the signals, there is no significant different between the original signal and reconstructed one when we used more than 85% of the data, when less than 85% of the data used, the reconstructed signals and the original signal are different. The sonograms generated from the reconstructed signals with random and non-uniform sampling are same as the original one, but there are some losses in contrast. The error of the reconstructed images was calculated, the result shows that the error in the image decreased with increasing the number of samples.