Let K and C be nonempty, closed and convex sets in R n and R m respectively and A be an m £ n real matrix. The split feasibility problem is to find u 2 K with Au 2 C: Many problems arising in the image reconstruction can be formulated in this form. In this paper, we use the auxiliary principle technique to suggest and analyze some new iterative algorithms for solving the split feasibility problems. Our new algorithms include the previously known ones as special cases. We also study the convergence criteria of these algorithms under some weaker conditions. In this respect, our results present a refinement and improvement of the previously known results.