Patent ID: 8886283

Claim:
A method of reconstructing an internal distribution of magnetic susceptibility values of an object, denoted by χ (x,y,z) and called a 3D map, by using a Computed Inverse Magnetic Resonance Imaging (CIMRI) tomographic procedure, comprising: a) acquiring a 3D complex-valued MR image of the object from a T2*-weighted MRI (T2*MRI) scan performed by a MRI scanning machine; b) extracting a 3D T2*MRI phase image, P(x,y,z;T E ), from the 3D complex-valued MR image; c) calculating a 3D magnetic field map, b(x,y,z), of the z-component (B z ) of a susceptibility-induced inhomogeneous magnetic field created by magnetizing the object in a main field, B 0 , from the MR phase image, P(x,y,z;T E ), under phase-unwrapped conditions or for phase-unwrapped images, according to: b ⁡ ( x , y , z ) = P ⁡ ( x , y , z ; T E ) γ ⁢ ⁢ T E where: γ=proton gyromagnetic ratio, and T E =echo time; and d) reconstructing a 3D magnetic susceptibility map, χ recon (r), of the object by performing a 3D deconvolution on the magnetic field map, b(r), according to: b ( r )= B 0 χ( r )* h 0 ( r ) and χ recon ( r )=b(r)* −1 h 0 (r)/B 0 where: r=(x,y,z) denotes 3D coordinates in space domain; the symbol * denotes a 3D convolution operator; the symbol * −1 denotes a 3D deconvolution operator; and h 0 (r) is a standard convolution kernel that is a point magnetic dipole kernel, according to: h 0 ⁡ ( r ) = 1 4 ⁢ ⁢ π ⁢ 3 ⁢ z 2 -  r  2  r  5 wherein performing the 3D deconvolution comprises executing a 3D Total Variation (TV) regularized iterative convolution scheme, which comprises solving a TV-regularized unconstrained minimization problem, according to: χ recon ⁡ ( r ) = min χ ∈ BV ⁢  χ ⁡ ( r )  TV + λ 2 ⁢  B 0 ⁢ χ ⁡ ( r ) * h 0 ⁡ ( r ) - b ⁡ ( r )  2 2 where: BV is a bounded variation function space, λ is a TV regularization parameter ∥•∥ TV denotes a TV norm, and ∥•∥ 2 2 denotes a L 2 norm; and wherein performing the 3D TV-regularized iterative convolution scheme comprises searching over all possible distributions χεBV to find an optimal χ-distribution, χ recon , which simultaneously minimizes both: a TV norm, and a data fidelity error measure; and further wherein a method for determining χ recon (r) comprises solving the 3D minimization problem by using a split Bregman iteration algorithm, according to: min d , v , χ ⁢  d ⁡ ( r )  TV + λ 2 ⁢  B 0 ⁢ v - b  2 2 + γ 1 2 ⁢  d - ∇ χ - a 1  2 2 ++ ⁢ γ 2 2 ⁢  v - h 0 * χ - a 2  2 2 with ⁢ ⁢ d = ∇ χ ⁢ ⁢ and ⁢ ⁢ v = h 0 * χ and, furthermore, wherein using the split Bregman iteration algorithm comprises transforming the 3D minimization problem into a series of three iteration sub-problems, and then solving each sub-problem by performing a Bregman-distance-based iteration with respect to three interim variables {‘d’, ‘v’, ‘χ’}; where: ‘d’ and ‘v’ are auxiliary variables, ‘χ’ is the magnetic susceptibility to be reconstructed, λ is the regularization parameter, and the parameters {‘γ 1 ’, ‘γ 1 ’, ‘a 1 ’, ‘a 2 ’} are introduced for efficient algorithm implementation and fast convergence.