Fig. 2. Graphical representation of principles of parallel imaging and compressed sensing.

In parallel imaging (A), uniform subsampling gives typical aliasing artifacts. Parallel imaging reconstruction makes it possible to achieve alias-free image. For SENSE, parallel imaging reconstruction is done in image space, whereas de-aliasing is already done before FFT in generalized autocalibrating partially parallel acquisitions (GRAPPA). In compressed sensing (B), variable-density, pseudo-random subsampling produces incoherent noise-like aliasing artifact after FFT. Sparsity (in this case, wavelet) transform allows setting of sparsity constraints. Image is obtained after IWT into image domain. IFFT back to k-space allows data consistency checking. After several iterations, final image is delivered with optimal balance between data consistency and sparsity constraints. FFT = Fourier transform, IFFT = inverse Fourier transform, IWT = inverse transform, PI = parallel imaging, SENSE = sensitivity encoding, WT = wavelet transform