Method for acquiring distorted experimental measurements of a physical phenomenon and reconstructing a first signal representing this physical phenomenon, said experimental measurements being obtained from a subject or object by magnetic resonance from the group composed of MRI, NMR spectroscopy or medical imaging such as CT scanning or PET scanning, the acquisition being distorted by a motion of the subject or object during the acquisition, said acquisition method implementing: - at least one acquisition of experimental measurements by at least one chain of acquisition by magnetic resonance or medical imaging of said experimental measurements, called measurements of primary interest, said acquisition chain comprising at least one distortion caused by said motion, - at least one model for simulating of said acquisition chain, said simulation model taking, as input, a second signal in a form chosen from a voxel, an image, an image stack and an MRI volume or medical imaging volume and supplying, as output, simulated experimental data , and - at least one distortion model of said distortion of said acquisition chain, said distortion model being determined at least from the experimental measurements themselves, said method being such that said simulation and distortion models comprise adjustable parameters dependent on the experimental measurements, said simulation and distortion models are coupled in the sense that the simulation model depends on the adjustable parameter of the distortion model , said method being characterized in that said adjustable parameters are optimized in a coupled manner, said optimization supplying, as output, the first signal and the parameters of the distortion model, said optimization producing a reconstruction of said first signal , in that the optimization of said parameters of the simulation model is produced by solving the inverse problem of the simulation model , taking the experimental measurements as inputs and solving the equivalent Hermitian symmetry problem, in that the signal originating from the solution of the inverse problem of the simulation model is used to generate a result of the simulation model , the difference between said experimental measurements of primary interest and said result of the simulation model is used as a criterion for optimizing said coupled simulation and distortion models, and a reconstruction residual is calculated from the difference between experimental measurements of primary interest and said result of the simulation model , and in that said reconstruction residual is modelled by a residual operator, said residual operator taking, as input, an estimation of the errors made on the parameters of the motion-distorted model and supplying, as output, said reconstruction residual , and being a function of the current parameters of the simulation and motion-distorted models. - at least one acquisition of experimental measurements by at least one chain of acquisition by magnetic resonance or medical imaging of said experimental measurements, called measurements of primary interest, said acquisition chain comprising at least one distortion caused by said motion, - at least one model for simulating of said acquisition chain, said simulation model taking, as input, a second signal in a form chosen from a voxel, an image, an image stack and an MRI volume or medical imaging volume and supplying, as output, simulated experimental data , and - at least one distortion model of said distortion of said acquisition chain, said distortion model being determined at least from the experimental measurements themselves, said method being such that <EOS>