We extend the so-called qeneralized Linear Sampling Method (GLSM) to the case of limited aperture data at a fixed frequency.in this case thefactorization of the samplig operatort does not obey the symmetry required in the justification of the GLSM introduced in Audibert-Haddar [Inverse Problems, 2014]. We propose a new formulation by adding an extra penalty term that asymptotically correct the non symmetry of the GLSM original penalty term. The analysis of the new formulation is first presented in an abstact fr—meworkF ‡e then show how to —pply our setting to the s™—l—r W pro˜lem with f—r eld me—surements or ne—r eld me—surements on — limited —pertureF ‡e n—lly IH v—lid—te the method through some numeri™—l tests in two dimensions —nd for f—r eld me—surementsF II Key words. snverse s™—ttering pro˜lemsD vine—r ƒ—mpling wethodD qener—lized vine—r ƒ—mpling wethodD p—™E IP toriz—tion wethodD u—lit—tive methods IQ