This paper is concerned with convergenceresults for the Linear Sampling method, a method in inversescattering theory characterizing an unknown obstacle directlythrough an indicator function computed from the data. Threeseperate but related results are shown. Firstly, sufficient con-ditions are formulated for the choice of the regularization pa-rameter that guarantee that the method converges in the pres-ence of noise for a sampling point inside the obstacle. Sec-ondly, a new, very strong connection to the related Factor-ization method is proved. Thirdly, for the first time the be-haviour of the indicator function for sampling points outsidethe obstacle is adequately explained.
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