1. Method for acquiring motion-disturbed experimental measurements of a physical phenomenon corresponding to experimental measurements obtained by a medical imaging or spectroscopy technique from the group consisting of MRI, NMR spectroscopy, scanner, and PET, and for reconstructing a reconstructed signal, the method implemented with a medical imaging or spectroscopy device comprising: at least one data acquisition process of obtaining raw data of said experimental measurements by said medical imaging or spectroscopy technique from the group consisting of MRI, NMR spectroscopy, scanner, and PET, said at least one data acquisition process comprising at least one disturbance, said at least one disturbance comprising a motion; at least one simulation model simulating said at least one data acquisition process, said at least one simulation model i) receiving, as input, a current signal ρ in a form of a voxel, an image, a stack of images, or a volume, the current signal ρ representing the physical phenomenon and being a function of the obtained raw data of the experimental measurements, and ii) providing, as output, simulated experimental data in a same form as a form of the obtained raw data of the experimental measurements, the form of the simulated experimental data and of the obtained raw data of the experimental measurements being distinct from a form of the current signal ρ; and at least one distortion model of said at least one disturbance of said data acquisition process, said at least one distortion model being determined at least from the experimental measurements obtained by the medical imaging or spectroscopy technique in said at least one data acquisition process, wherein, said simulation and distortion models comprise distinct adjustable parameters dependent on the experimental measurements obtained by the medical imaging or spectroscopy technique in said at least one data acquisition process, said distinct adjustable parameters comprising i) the current signal ρ and ii) parameters α of the distortion model, said simulation and distortion models are coupled in the sense that the simulation model depends on the adjustable parameters α of the distortion model, and said adjustable parameters ρ and α are optimized jointly, the optimization providing, as output, i) the reconstructed signal corresponding to an optimized current signal ρ and representing a result of the reconstructed signal corrected of distortions, and ii) the parameters α of the distortion model, wherein the optimization of said parameters of the at least one simulation model is carried out by solving an inverse problem of the at least one simulation model, taking the experimental measurements as inputs and solving an equivalent Hermitian symmetry problem, wherein, the current signal issued from the solution of the inverse problem of the at least one simulation model is used to generate the simulated experimental data, a difference between said experimental measurements and said simulated experimental data is used as optimization criterion for said coupled simulation and distortion models, and a reconstruction residual is calculated from the difference between said experimental measurements and said simulated experimental data, and wherein said reconstruction residual is modeled by a residual operator, said residual operator taking an estimate of errors of the parameters of the distortion model as input and providing said reconstruction residual as output, and being a function of current parameters ρ and α of the simulation and distortion models.