​The main of the chall​​enge of Magnetic Resonance Imaging (MRI) is dealing with high levels of noise which may corrupt the image especially since the noise is almost correlated with the image details. In this regard, we propose a new MRI enhancement method to overcome this limitation. The proposed MRI enhancement method relies on square sub-images enhancement depending on the noise level in each position using spatial adaptation of the Semi-Classical Signal Analysis (SCSA) method, where an enhancement parameter h is subject to a Gaussian distribution. ​

​The idea of the modulating function-based method (MFBM) is to multiply the considered differential equation by a set of modulating functions to transform the differential equation into a set of algebraic integral equations by applying integration by parts, where the unknown initial conditions are eliminated by the properties of the modulating functions. The method does not require solving the direct problem by which the computational cost is reduced. Further, approximating the derivatives of the measurements, which are usually noisy, is avoided with this method. ​​