... We have applied the Pixon Based Image Restoration Method (Puetter, this volume; Pi?a 1993, 1992; Puetter ?a 1993) to real and simulated HST Spectra. ... An undesirable characteristic of most restoration techniques is the noise amplification, over-resolution and ringing. ... Ringing is especially bad in the vicinity of emission lines, where the slope of the continuum changes significantly. ... The advantage of this technique is that we can impose upper and lower bounds, namely positivity and...