Adaptive ℓ₀-norm sparse third order volterra filter for transcranial ultrasound image enhancement: In-vivo results

Differentiating between the early stages of Parkinson's Disease (PD) and other diseases with parkinsonian symptoms is difficult from analyzing motor degeneration symptoms alone. For this reason, a commonly used diagnostic marker for PD is the hyperechogenicity of the Substantia Nigra (SN), which can help to make an early differential diagnosis of PD. Current practice for determining if an image displays hyper-echogenicty relies on clinician experience heavily because of the difficulty of discerning features in standard B-mode imaging. Harmonic imaging has been studied extensively, and while it does improve the image quality, it suffers from spectral overlap with the noisy fundamental component. Our approach uses an adaptive Third Order Volterra Filter (ToVF), which avoids this problem by completely separating an image into its linear, quadratic, and cubic components with no overlap. One of the standard implementations of the ToVF is through an adaptive Recursive Least Squares (RLS) algorithm. This paper examines two algorithms developed through applying an ℓ₀ constraint on the standard RLS cost function. The two algorithms approximate this cost function in different ways, one using a Slow Time Varying (STV) approximation and the other using a Taylor Series Expansion (TSE) approximation. Theoretically the ℓ₀ constraint will shorten the number of iterations to reach steady state without sacrificing image quality. Our results confirm that these theoretical results hold on an in vivo application.