Main Noise Source
INCORRECT. Electronic circuitry can generate extraneous RF fields which can produce certain image artefacts, but this is not usually an issue.
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INCORRECT. Off-resonance effects refers to any signal that has a frequency different to that which expected in an ideal MRI system, with a perfectly homogenous static magnetic field in the sample or patient, and perfectly linear magnetic field gradients. For example, variations of the static magnetic field which arise from susceptibility differences between tissues causes variations in the Larmor frequency. This may result in image artefacts (which are a form of structured noise). However, off-resonance effects are not the principal source of noise in MRI.
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CORRECT. The magnetic resonance signal is an electromotive force induced in a coil by a rotating magnetic moment of nuclear spins. The signal level must be well above noise levels to produce clinically useful MR images, and yet this signal is very weak.
Image noise originates (i) in the patient or object to be imaged, and (ii) is added during the processing of the signal in the receiver chain. In the receiver chain, noise may be generated in the preamplifier and at the connection between the preamplifier and the RF receive coil. In the RF coil, which is a conductor, thermal noise is produced by the stochastic motion of free electrons. This motion is caused by ohmic losses in the RF coil itself, and by eddy current losses in the patient, which are inductively coupled to the RF coil. (High conductivity of receiver coils avoids noise, whereas conduction in the patient causes noise.)
The resistance induced in the receiving circuit by eddy currents in the patient (called loading) is much more significant in a modern high-field MRI system than a receiver coil's own resistance. A larger mass in vivo causes greater coil loading—and more noise.
The signal available in a magnetic resonance experiment is dependent on many factors, including tissue specific parameters, such as T1, T2 and proton density, and the choice of pulse sequence parameters, such as the echo time (TE), repetition time (TR), flip angle, preparation-pulse delay time (if applicable), number of measurements, et cetera.
Further reading on this topic:
Books: MRI From Picture to Proton p66, MRI: Physical Principles & Sequence Design p332