  I employ the Lucy rectification algorithm to recover the
inclination-corrected distribution of local disk galaxies in the plane of
absolute magnitude ($M_i$) and HI velocity width ($W_{20}$). By considering the
inclination angle as a random variable with a known probability distribution,
the novel approach eliminates one major source of uncertainty in studies of the
Tully-Fisher relation: inclination angle estimation from axial ratio.
Leveraging the statistical strength derived from the entire sample of 28,264
HI-selected disk galaxies at $z < 0.06$ from the Arecibo Legacy Fast ALFA
(ALFALFA) survey, I show that the restored distribution follows a sharp
correlation that is approximately a power law between $-16 > M_i > -22$: $M_i =
M_0 - 2.5\beta \ [\log(W_{\rm 20}/250 {\rm km/s})]$, with $M_0 = -19.77\pm0.04$
and $\beta = 4.39\pm0.06$. At the brighter end ($M_i < -22$), the slope of the
correlation decreases to $\beta \approx 3.3$, confirming previous results.
Because the method accounts for measurement errors, the intrinsic dispersion of
the correlation is directly measured: $\sigma(\log W_{20}) \approx 0.06$ dex
between $-17 > M_i > -23$, while $\sigma(M_i)$ decreases from $\sim$0.8 in slow
rotators to $\sim$0.4 in fast rotators. The statistical rectification method
holds significant potential, especially in the studies of
intermediate-to-high-redshift samples, where limited spatial resolution hinders
precise measurements of inclination angles.
