Adjoint image warping using multivariate splines with application to four-dimensional computed tomography.

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• Adjoint image warping is crucial for solving image reconstruction problems, particularly in four-dimensional computed tomography (4D-CT).
• Current methods often rely on approximations for the adjoint of image warping, impacting reconstruction accuracy and efficiency.
• Efficient and accurate adjoint computation is needed for advanced imaging models.

Purpose of the Study:

• To introduce an efficient implementation of the exact adjoints of multivariate spline-based image warping.
• To compare this new method against previously used approximate alternatives in 4D-CT reconstruction.
• To demonstrate improvements in memory usage, computation time, and reconstruction quality.

Main Methods:

• Computed a matrix representation of trivariate cubic image warping using symbolic computer algebra.
• Developed an efficient, low-memory implementation of the adjoint action via on-the-fly matrix computation and parallelized matrix multiplication.
• Applied the exact adjoint operator to a 4D-CT reconstruction model comparing single subscan images against multiple subscan projection data.

Main Results:

• The proposed method requires half the memory compared to methods storing approximate motion inverses.
• It eliminates the need for motion inversion computation and associated tunable parameters.
• Achieved similar or better reconstruction quality than more computationally expensive methods, especially for large motion, and superior quality to simpler methods.

Conclusions:

• The implementation of the exact adjoint of cubic image warping enhances computational efficiency.
• This method provides accurate image reconstructions in demanding scenarios like 4D-CT.
• Offers a more effective solution for image warping in forward models.