Myriad and meridian functionals as extreme forms of smoothed quasinorms

Problem of filtering of piecewise constant signal corrupted by additive Gaussian or Laplacian noise is considered. Efficiency of functionals of minimum duration based on quasinormed spaces is analyzed. Advantages of smoothed modifications of quasinorms are demonstrated. It is shown, that myriad and meridian filtering are limit forms of smoothed-quasinorm ones. The new class of generalized logarithmic filtering methods is proposed by generalization of myriad and meridian methods.