Abstract: Blurring and noise are serious problems in hydro-test with high-energy X-ray radiography and make it difficult to reconstruct density distributions from radiographic images. A constrained optimization reconstruction method to decrease the blurring and noise impact is proposed. In this method, the parallel-beam X-ray projections are modeled by inserting a blurring matrix in. The optimization reconstruction problem is minimized by steepest descent method, and a preconditioned matrix has been adopted to improve the reconstruction efficiency. We focus on the topographic reconstruction of piecewise smooth objects involving sharp edges, so the algorithm is based on generalized-variation-minimization constraints, piecewise constraints and the non-negative density values constraints. We applied the reconstruction algorithm to reconstruct computer-synthesized images of the French Test Object (FTO) and a hydro-test object image. The results show that our method is beneficial to improve the quality of reconstructed image with better performance of noise smoothing and better edge preserving as well.