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The process of restoring signal resolution to data recorded from a sluggish measuring device may be accomplished by appropriate mathematical operations on the data using a large digital computer. Smoothing techniques may be applied in the transform domain to derive an inverse convolver to be used in real space. The inverse convolver, a non-physically realizable filter function, when convolved with the output of the device, restores high-frequency components necessary for sharp detail. Only knowledge of the impulse response of the device and the recorded data is required. In applications to data of the type found in many geophysical systems impressive results are obtained even in the presence of considerable random noise. This procedure represents a different approach to the approximation required by the process and has advantages in the ease and simplicity with which it may be applied.