Method of reconstructing magnetic resonance image data

A method of reconstructing a magnetic resonance (MR) image from k-space data, the method comprising:

• providing a computer with k-space data of an image of a subject;
• and
• in said computer, performing a reconstructing algorithm, using a sparse image coding procedure in order to reconstruct, the MR image from the k-space data with iterative optimization comprising:
• a data consistency iteration step comprising a determination of a difference between the reconstructed MR image transformed into k-space and the provided k-space data, wherein the determination of the difference comprises determining an l2-norm of the result of the difference between the provided k-space data and the reconstructed MR image transformed into k-space;
• and
• a denoising iteration step applied to an MR image generated by the data consistency iteration step, wherein the denoising iteration step incorporates a sparsifying operation to provide a sparse representation of the MR image for the imaged region as an input to the data consistency iteration,
• wherein the denoising iteration step is of the form
• x
• ^
• =
• arg
• ⁢
• ⁢
• min
• x
• ⁢
• h
• ⁡
• (
• x
• )
• ,
• h
• ⁡
• (
• x
• )
• ,
• h(x) is a function defined as {sparse consistency component in image space+λ(sparse coefficients associated with a synthesis dictionary for the sparse representation of the MR image data)}, and λ is a sparsity-control parameter a value of which is adjustable to adjust a strength of sparsity for the sparse representation of the MR image.