Method for optimized bias and signal inference in magnetic resonance image analysis

A method for highly reliable inference of signal and bias in weighted images, the weighted images being at least one of diffusion weighted, echo time weighted and repetition time weighted images, said method comprising the steps of:

• a) providing a magnetic resonance imaging apparatus capable of operation at different encoding levels;
• b) acquiring a set of magnitude signal decays from a patient using said magnetic resonance imaging apparatus at each of a selected plurality of encoding levels distributed across a range of encoding levels within its capability, each said set of signal decays being representative of an image of a preselected cross-section of the patient, and each said signal decay of each said set corresponding to a pixel of its associated image;
• c) initializing or setting the value of noise σg for each pixel to 0 or a suitable very small value;
• d) processing said acquired or bias-corrected signal decays on a pixel by pixel basis to obtain the best possible fit between them and a non-mono-exponential equation wherein a non-linear least-squares method is used to obtain a fit;
• e) determining θi=ŝi/σg for each fitted signal ŝi as an estimate for the signal-to-noise ratio at each measured signal si;
• f) obtaining for each pixel a first estimation of noise σg, taking into account the non-linear behavior of the noise distribution in relation to a true signal;
• g) determining for each pixel the Rician signal bias bi for each fitted signal level ŝi determined in d);
• h) obtaining for each pixel a bias-corrected signal value sic by subtracting the Rician signal bias bi determined in g) from the measured signal level si acquired in b);
• i) repeating steps d) to h) until the change of sic falls under a predefined threshold.

An apparatus for highly reliable inference of signal and bias in weighted images, the weighted images being at least one of diffusion weighted, echo time weighted and repetition time weighted images, said apparatus comprising a controller arranged to:

• a) receiving a set of magnitude signal decays from a patient obtained by a magnetic resonance imaging apparatus at each of a selected plurality of encoding levels distributed across a range of encoding levels within its capability, each said set of signal decays being representative of an image of a preselected cross-section of the patient, and each said signal decay of each said set corresponding to a pixel of its associated image;
• b) initializing or setting the value of noise σg for each pixel to 0 or a suitable very small value;
• c) processing said acquired or bias-corrected signal decays on a pixel by pixel basis to obtain the best possible fit between them and a non-mono-exponential equation, wherein a non-linear least-squares method is used to obtain a fit;
• d) determining θi=ŝi/σg for each fitted signal ŝi as an estimate for the signal-to-noise ratio at each measured signal si;
• e) obtaining for each pixel a first estimation of noise σg, taking into account the non-linear behavior of the noise distribution in relation to a true signal;
• f) determining for each pixel the Rician signal bias bi for each fitted signal level ŝi determined in c)
• g) obtaining for each pixel a bias-corrected signal value sic by subtracting the Rician signal bias bi determined in f) from the measured signal level si acquired in a);
• h) repeating steps c) to g) until the change of sic falls under a predefined threshold.