In inverse problems, when the forward map is a smoothing
(regularizing) operator,
the inverse map is usually unbounded. Thus only the low frequency
component of the object of interest is accessible from noisy measurements.
In many inverse problems however, the neglected high frequency component may
significantly affect the measured data. Using simple scaling arguments,
we characterize the influence of the high frequency component.
We will then show how to eliminate the effect of the high frequency
component in a one-dimensional inverse spectral problem to
obtain better reconstructions of the low frequency component of
the unknown. Numerical results with synthetic data will be presented.