Compressive sensing is the reconstruction of sparse images

or signals very few samples, by means of solving a

tractable optimization problem. In the context of MRI, this

can allow reconstruction many fewer k-space samples,

thereby reducing scanning time. Previous work has shown

that nonconvex optimization reduces still further the number

of samples required for reconstruction, while still being

tractable. In this work, we extend recent Fourier-based algorithms

for convex optimization to the nonconvex setting, and

obtain methods that combine the reconstruction abilities of

previous nonconvex approaches with the computational speed

of state-of-the-art convex methods.

-Compressive sensing is the reconstruction of sparse images

or signals　very few samples, by means of solving a

tractable optimization problem. In the context of MRI, this

can allow reconstruction　many fewer k-space samples,

thereby reducing scanning time. Previous work has shown

that nonconvex optimization reduces still further the number

of samples required for reconstruction, while still being

tractable. In this work, we extend recent Fourier-based algorithms

for convex optimization to the nonconvex setting, and

obtain methods that combine the reconstruction abilities of

previous nonconvex approaches with the computational speed

of state-of-the-art convex methods.