Frequency Domain Compressive Sampling for Ultrasound Imaging
Figure 3
(a) A full US RF signal and (b) its sparse representation via Fourier transform. (c) Sampling 30% of the US RF signal using a basis of random Diracs (crosses), maximally incoherent with the Fourier basis, leads to (d) a dense signal in the sparsifying basis (Fourier transform). However, (e) sampling 30% of the US RF signal using a basis of random sinusoids (circles), coherent with the sparsifying basis, is equivalent to sample random Fourier coefficients of the signal. (e) The resulting measurements in the sparsifying basis (Fourier transform) are sparse as well.
