In automatic target recognition applications, an important task is to obtain denoised signal of the object. In this paper, the reconstruction of 1D deterministic signals, for example, range profiles, corrupted by random signal shift and additive white Gaussian noise using 2D bispectrum is considered. Combined bispectrum-filtering techniques based on smoothing the noisy bispectrum estimates by 2D linear and nonlinear filters are proposed. It is shown that bispectrum estimates obtained by the conventional direct bispectrum estimator are corrupted by fluctuation errors and are biased. The performance of the proposed bispectrum-based signal reconstruction methods is analyzed using two conventional criteria - the reconstructed signal fluctuation variance and bias. The numerical simulation results show that 2D filtering of real and imaginary components of noisy bispectrum estimates is most efficient in the sense of minimum MS errors.