Frequency-dependent ultrasound attenuation estimation with spatial regularization and monotonicity constraints

Ultrasound attenuation is frequency dependent, and its non-linear frequency dependence can be characterized by a power-law model, α ( f ) = α 0 f η , where α ( f ) is the attenuation at frequency f , α 0 is the attenuation magnitude, and η is the frequency exponent that governs the degree of frequency dependence. The frequency dependence of attenuation is correlated with underlying tissue structure and can be used as a clinically useful biomarker. Existing attenuation estimation methods often assume linear frequency dependence, limiting their ability to capture the nonlinear behavior of attenuation. We propose a broadband attenuation estimation framework that combines spatial regularization with monotonicity constraints across frequency. The method employs a multi-band modeling approach, dividing the bandwidth into overlapping sub-bands and enforcing monotonicity during reconstruction to preserve the natural increasing trend of attenuation with frequency. The proposed method was evaluated on simulated data and ex vivo bovine skeletal muscle, spanning a broadband frequency range (2–20 MHz), and compared against two benchmarks: Spatially Weighted Total Variation regularization for Attenuation Coefficient Estimation (SWTV-ACE) and MultiBand Attenuation Coefficient Estimation (MB-ACE) methods. Simulation results show that the proposed method significantly reduces mean absolute percentage error (MAPE) for both attenuation parameters, α 0 and η , and achieves the lowest root-mean-square error in power-law fitting over a wide range of ground truth attenuation values. For bovine muscle, the method demonstrated high-fidelity reconstruction of the power-law frequency dependence, with estimated attenuation points closely following the fitted curve (coefficient of determination, R 2 = 0 . 99 ), with parameter values aligning with reported literature. • We propose an attenuation estimation method using frequency monotonicity and spatial regularization. • Improved attenuation parameter estimation ( α 0 , η ) with superior power-law fit. • Enables accurate, physically consistent broadband attenuation estimation.