= Solution
TODO: Biology deferred at the user's request: clinical contrast interpretation, applications, and the head-injury MRI-versus-CT comparison.
The generic physics of <magnetic resonance imaging> combines a main static magnet, radiofrequency transmit and receive coils, controlled <magnetic field gradients>, signal electronics and reconstruction. A transverse radiofrequency pulse excites <nuclear spins> near their Larmor <frequency>, $\omega_0=\gamma B_0$. The evolving transverse magnetization induces a received signal; <phase> coherence and relaxation determine its time dependence.
Gradients encode <position> into <phase>. In a simplified homogeneous receive-sensitivity model,
$$
s(t)=\int\rho(\mathbf r)e^{-2\pi i\mathbf k(t)\cdot\mathbf r}\,d^3\mathbf r,
\qquad \mathbf k(t)=\frac{\gamma}{2\pi}\int^t\mathbf G(t')\,dt'.
$$
Here $\mathbf k$ is in cycles per unit length and $\gamma$ is in radians per second per tesla. Echo sign changes, pulse sequence timing and receive sensitivity belong in a more complete signal model. Sampling this <MRI k-space> and reconstructing its data produces an image; the measured samples are not already real-space pixel values.
The physical signal depends on <spin> density, longitudinal recovery and transverse dephasing. Timing changes their weighting. Static field inhomogeneity adds reversible dephasing beyond intrinsic <transverse relaxation>, motivating echo techniques and distinguishing $T_2^*$ from $T_2$. Those are physical signal mechanisms; their biological interpretation remains deferred.
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