Patent ID: 7230429

Claim:
A method for producing sensitivity maps, comprising: receiving an original plurality of sensitivity maps u j o corresponding to a plurality of coils in an imaging system, where u j o corresponds to the j th coil; minimizing an energy functional, where the energy functional E[u j |u j o , D] is given by E [ u j ⁢  u j 0 , D ] = 1 2 ⁢ ∑ j ⁢ ∫ Ω ⁢ λ D j ⁡ ( x ) ⁢ ( u j ⁢ I - I j ) 2 ⁢ ⁢ ⅆ x + γ ⁢ ∑ j ⁢ ∫ Ω ⁢  ▽ ⁢ ⁢ u j  P ⁡ ( x ,  ▽ ⁢ ⁢ u j  ) ⁢ ⁢ ⅆ x + μ 2 ⁢ ∫ Ω ⁢ ( ∑ j ⁢ u j 2 - 1 ) 2 ⁢ ⁢ ⅆ x wherein u j is an inpainted sensitivity map for the J th coil and D is the dark regions of u j o where ∑ j ⁢ ∫ Ω ⁢ λ D j ⁡ ( x ) ⁢ ( u j ⁢ I - I j ) 2 ⁢ ⁢ ⅆ x is where is the fidelity term, ∑ j ⁢ ∫ Ω ⁢  ▽ ⁢ ⁢ u j  P ⁡ ( x ,  ▽ ⁢ ⁢ u j  ) ⁢ ⁢ ⅆ x is the smoothing term, and ∫ Ω ⁢ ⁢ ( ∑ j ⁢ u j 2 - 1 ) 2 ⁢ ⅆ x is the sum of squares of the sensitivity maps; where u j o is the image generated by coil j, wherein u j o is defined as I j /I, where I j is the image generated by coil j and the homogeneous image, I , is the square root of the sum of squares of I j , where γ and μ balance the terms in the energy functional, wherein increasing γ results in a smoother image, wherein maximizing μ brings the term ∫ Ω ⁢ ⁢ ( ∑ j ⁢ u j 2 - 1 ) 2 ⁢ ⅆ x closer to unity, applying v =(v 1 , v 2 ) is a vector field and h is the step space for this field div ⁡ ( v _ ) = Δ - x ⁢ ν 1 + Δ - y ⁢ ν 2 h , where the Euler-Lagrange equation for the energy functional, where the Euler-Lagrange equation for the energy functional is λ D j ⁡ ( x ) ⁢ ( u j ⁢ I - I j ) ⁢ I - γ ⁢ ⁢ ▽ . (  ▽ ⁢ ⁢ u j  P - 2 ⁢ P ⁢ ⁢ ▽ ⁢ ⁢ u j ) + μ ( 1 - 1 ∑ j ⁢ μ j 2 ) ⁢ u j = 0 with boundary condition ∂u j /∂ n =0, for the j th coil, where n is the outward unit normal to the image boundary, to produce an iteration formula corresponding to the Euler-Lagrange equation for the energy function, wherein the iteration formula is u j n + 1 = γ ⁡ [ C 1 ⁢ u k + 1 , l n , j + C 2 ⁢ u k - 1 , l n , j + C 3 ⁢ u k , l + 1 n , j + C 4 ⁢ u k , l - 1 n , j ] + λ D j ⁢ I j ⁢ I λ D i ⁢ I 2 + γ ⁡ ( C 1 + C 2 + C 3 + C 4 ) + μ ( 1 - 1 ∑ j ⁢ u j 2 ) where C 1 = p kl a kl , C 2 = p k - 1 , l a k - 1 , l , C 3 = p kl b kl , C 4 = p k , l - 1 b k , l - 1 a kl = ( ( Δ + x ⁢ u kl n ) 2 + ( u k , l + 1 n - u k , l - 1 n 2 ) 2 ) 2 - p kl 2 b kl = ( ( Δ + x ⁢ u kl n ) 2 + ( u k + 1 , l n - u k - 1 , l n 2 ) 2 ) 2 - p kl 2 where j corresponds to the j th coil, k,l correspond to rows and columns of the image u respectively, and n corresponds to the n th iteration; providing an initial guess for u j , wherein the initial guess for u j comprises the raw sensitivity maps for each coil: u j ⁢ _raw ⁢ ( x ) = { I j ⁡ ( x ) I ⁡ ( x ) , x ∉ D guess , x ∈ D ; and iterating the iteration formula to minimize the energy functional.