Abstract: Scattered data reconstruction has been widely studied in the fields of signal processing and
computer graphics. Moreover, in recent years, to obtain sparse representation approximations of
scattered data by means of sparse optimization method has also become a hot spot in the
cross-domain of optimization and surface reconstruction. In this paper, we establish the connection
between surface fitting of scattered data and the piecewise sparseness in PSI space generated by a
B-spline, and introduce the piecewise sparsity to the Bregman inverse scale space (ISS) algorithm. In
addition, an adaptive piecewise ISS algorithm is established to solve the scattered data reconstruction
problem. Through the analysis of the piecewise symbolic consistency, the performance guarantee of
adaptive piecewise ISS system is obtained in this paper and the selection of aP_ISS parameters can be
avoided. Numerical experimental results applied to the surface reconstruction of scattered data show
that, this algorithm can not only effectively fit the surface, but also protect the piecewise sparsity of
coefficient of the surface.

Key words: scattered data reconstruction, piecewise sparsity, inverse scale space, sparse optimization