Unifying reconstruction and motion estimation in first pass cardiac perfusion imaging

A system to process perfusion images to correct motion effects, comprising:

• a memory, enabled to store data:
• a processor, enabled to execute instructions to perform the steps:
• receiving undersampled image data of a dynamic scene of a first-pass cardiac perfusion MRI;
• minimizing a single objective function that combines at least three terms, each term depending on image data representing a true dynamic scene, wherein a first term expresses a motion estimation related to the undersampled image data, a second term expresses a temporal constraint and a third term expresses a spatial constraint and minimizing the objective function by constraining the temporal constraint term and the spatial constraint term and applying a penalizing term that penalizes a violation of the constraining;
• and
• generating data representing a reconstructed perfusion image corrected for motion based on the minimized single objective function.

A method for processing perfusion images to correct motion effects, comprising:

• a processor receiving undersampled image data of a dynamic scene of a first-pass cardiac perfusion MRI;
• the processor minimizing a single objective function that combines at least three terms, each term depending on image data representing a true dynamic scene, wherein a first term expresses a motion estimation related to the undersampled image data, a second term expresses a temporal constraint and a third term expresses a spatial constraint;
• and
• the processor generating data representing a reconstructed perfusion image corrected for motion based on the minimized single objective function,
• wherein the objective function is expressed as:
• |Af−b|22+γ|(Df)t|22+μ|Tf|,
• wherein
• f is a vector representing the true dynamic scene related to the undersampled image data,
• A is an operator specifying an undersampling Fourier task,
• b is a vector representing the undersampled image data,
• D is a deformation operator,
• T is a spatial total variation operator,
• (.)t is a first order temporal derivative operator,
• γ a regularization factor, and
• μ is a tuning parameter.