Regularization methods for solving third-order volterra filter with improved convergence speed: In-vivo application

The differential diagnosis of idiopathic Parkinson's Disease (iPD) from atypical parkinsonian syndromes can be very difficult at the early stages of these diseases. Trancranial Ultrasound Imaging (TCUI) of the Substantia Nigra (SN) is one method that has been shown to aide in this early differential diagnosis. TCUI is done to detect hyperechogenicity in the SN, which is defined as an echogenic area above a threshold size of 0.2 cm2. Because B-mode ultrasound images are often noisy, determining the size of the echogenic area can be difficult. Harmonic imaging using a Third-Order Volterra (ToVF) filter is one solution that has been successful in filtering out the noise in these images, allowing a more reliable diagnosis. In this paper, we show that regularization methods such as Truncated Singular Value Decomposition (TSVD) and Tikhonov method can be used to solve for the Volterra Filter's coefficient much more quickly than least mean square (LMS) methods studied previously without sacrificing image quality. This finding has implications in terms of the Volterra Filter's viability for use in real-time harmonic imaging applications.

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