  Pulse-echo Quantitative ultrasound (PEQUS), which estimates the quantitative
properties of tissue microstructure, entails estimating the average attenuation
and the backscatter coefficient (BSC). Growing recent research has focused on
the regularized estimation of these parameters. Herein, we make two
contributions to this field: First, we consider the physics of the average
attenuation and backscattering to devise regularization terms accordingly. More
specifically, since the average attenuation gradually alters in different parts
of the tissue while BSC can vary markedly from tissue to tissue, we apply L2
and L1 norms for the average attenuation and the BSC, respectively. Second, we
multiply different frequencies and depths of the power spectra with different
weights according to their noise levels. Our rationale is that the
high-frequency contents of the power spectra at deep regions have a low
signal-to-noise ratio. We exploit the alternating direction method of
multipliers (ADMM) for optimizing the cost function. Qualitative and
quantitative evaluation of bias and variance exhibit that our proposed
algorithm substantially improves the estimations of the average attenuation and
the BSC.
