SEISMIC DATA ARE BAND-LIMITED, THEREFORE ONE CAN USE ONLY A PARTIAL SET OF FREQUENCY COEFFICIENTS IN THE RANGE OF REFLECTIONS BAND, WHERE THE SIGNAL-TO-NOISE RATIO IS HIGH AND SPATIAL ALIASING IS LOW, TO RECONSTRUCT THE ORIGINAL WAVE FIELD. FURTHERMORE, LOW-FREQUENCY CHARACTERISTICS OF THE COHERENT GROUND ROLLS ALLOWS DIRECT ELIMINATION OF THEM DURING RECONSTRUCTION BY DISREGARDING THE CORRESPONDING FREQUENCY COEFFICIENTS (USUALLY BELLOW 10 HZ) VIA A FREQUENCY MASK. IN THIS PAPER, A NON-LINEAR ALGORITHM IS PROPOSED WHICH ADDRESSES SOME CHALLENGES OF SPATIAL SAMPLING, RECONSTRUCTION, AND DENOISING IN SEISMIC EXPLORATION. NUMERICAL EXPERIMENTS FROM BOTH SIMULATED AND REAL FIELD DATA ARE INCLUDED TO ILLUSTRATE THE EFFECTIVENESS OF THE PRESENTED METHOD.