In　this　paper,　a　Cauchy　problem　for　two-dimensional　Lap　lace　equation　in　the　strip　0　≤　x　≤　1　is　considered.　This　is　a　classical　severely　ill-posed　problem.　Connecting　Shannon　wavelet　bases　with　a　spectral　integral　of　the　Hermitian　operator,　we　can　obtain　a　regularized　solution.　Moreover,　some　sharp　stable　estimates　between　the　exact　solution　and　it＇s　approximation　is　also　provided.　©　2012　IEEE.