We propose here a new approach together with a corresponding class of algorithms for offline estimation of linear operators mapping input to output signals. The operators are modelled as multipliers, i.e. linear and diagonal operator in a frame or Bessel representation of signals (like Gabor, wavelets ...) and characterized by a transfer function. The estimation problem is formulated as a regularized inverse problem, and solved using iterative algorithms, based on gradient descent schemes. Various estimation problems, which differ by a choice for the regularization function, are studied in the case of Gabor multipliers. The transfer function actually provides a meaningful interpretation of the differences between the two signals or signal classes under consideration, and examples are discussed. Furthermore, examples of signal transformations with such Gabor transfer functions are also given.