We　consider　the　problem　of　determining　an　unknown　source,　which　depends　only　on　the　spatial　variable,　in　a　diffusion　equation.　This　is　an　ill-posed　problem.　For　a　reconstruction　of　the　solution　from　indirect　data.,　the　dual　least　squares　method　generated　by　the　family　of　Shannon　wavelet　subspaces　is　applied.　Moreover..　a　certain　simple　nonlinear　modification　of　the　method　based　on　local　refinements　of　the　wavelet　expansion　of　the　noisy　data　is　investigated.