A computationally efficient discrete Backus-Gilbert (BG) method is derived that is appropriate for resolution-matching applications using over-sampled data. The method in its current form is restricted to a resolution-only minimization constraint, but in the future could be extended to use a simultaneous noise minimization constraint using a generalized singular value decomposition approach. In 1-D simulated comparisons, the discrete BG method can be 250% more efficient than the original BG method while maintaining similar accuracies. In addition, a singular value decomposition approximation increases the computational efficiencies an additional 43% to 106%, depending upon the scene. The ability to recompute the modified BG coefficients dynamically at lower computational cost make this work applicable toward applications in which noise may vary, or where data observations are not available consistently (e.g., in RFI contaminated environments).