Figure 5: Compressive sensing X-ray tomography: the Logan-Shepp phantom and its least squares reconstruction after Tomography Central Lice Theorem composing 1-D Fourier-sampling projection along 22 radial lines (here / ) into 2-D sparse spectrum which are then Fourier inverted to produce a sharp image under the norm minimization (bottom right) better than the norm (top right). , assuming that has norm less than some error tolerance . MRI Fourier Tomography Reconstruction with 5% sparse sampling using an energy LMS constraint versus magnitude convex hull constraint for tomography projection measurements and inverted such an underdeterminant rectangular matrix equation of degree by a linear programming, under a surrogate norm minimization of total number of nonzero pixels (irrespective to their values to select only an inhomogeneous solution without the arbitrary mixing homogenous ones). They use purely random unstructured sampling mask of ones for about degree of freedoms among all zeros, to make linear measurements and invert the underdeterminant Mask matrix equation. We follow the convention of electrodes (see V1 to V6 Figure 6).