Module iharperella 

HARPERELLA and iHARPERELLA — integrated phase unwrapping and background field removal

Both algorithms simultaneously unwrap phase and remove background field by estimating the phase Laplacian outside the brain. The background phase is harmonic inside the brain (nabla^2 phi_bg = 0), so the wrapped Laplacian inside the brain contains only tissue sources.

HARPERELLA estimates the exterior Laplacian by making the SMV of the total Laplacian uniform across the FOV (Eq [3] in the paper): min ||S(nabla^2 phi_E) + S(nabla^2 phi_brain) - delta||_2

iHARPERELLA instead directly minimizes the weighted resulting phase (Eq [3] in the ISMRM abstract): min ||W * inv_lap(nabla^2 phi_brain + nabla^2 phi_out)||_2 providing more robust low-frequency background suppression.

References:

• HARPERELLA: Li, W., et al. (2014). “Integrated Laplacian-based phase unwrapping and background phase removal for quantitative susceptibility mapping.” NMR in Biomedicine, 27(2):219-227. doi:10.1002/nbm.3056
• iHARPERELLA: Li, W., Wu, B., Liu, C. (2015). “iHARPERELLA: an improved method for integrated 3D phase unwrapping and background phase removal.” Proc. ISMRM 23, p.3313.

Structs

HarperellaParams

HARPERELLA / iHARPERELLA algorithm parameters

Functions

apply_inv_lap 🔒

Apply inverse Laplacian using pre-computed eigenvalues

apply_smv 🔒

Apply SMV filter in k-space: S(x) = ifft(s_fft * fft(x))

cg_solve_masked 🔒

Generic CG solver for masked normal equations

compute_laplacian_eigenvalues 🔒

Compute discrete Laplacian eigenvalues for inverse Laplacian

compute_smv_fft 🔒

Compute FFT of SMV kernel (returns real part, since kernel is symmetric)

harperella

HARPERELLA — integrated phase unwrapping and background removal

iharperella

iHARPERELLA — improved integrated phase unwrapping and background removal

iharperella_with_weights

iHARPERELLA with custom W_Brain weighting

prepare_laplacian 🔒

Compute wrapped Laplacian, erode mask, prepare interior/exterior masks

solve_poisson 🔒

Solve Poisson equation via FFT: nabla^2 u = f -> u

Type Aliases

IharperellaParams

Type alias for backwards compatibility