In a non-destructive estimation using topological derivatives, candidate cracks are found from the distribution of the toological derivatives. A determination of correct cracks from the candidate cracks using LASSO is considered in this paper. We compute the coefficient matrix using BEM for 2D Laplace crack problems in two ways and determine the correct cracks solving the algebraic equation for the sparse vector. By solving numerical examples, we can estimate the correct cracks in two cases of the coefficient matrix. Moreover, in the case of candidate cracks having similar directions and very close location, we can determine the correct crack with sufficient accuracy assuming the presence of one of each candidate cracks in the domain and calculating the coefficient matrix.