The difference between the early stages of Parkinson's Disease (PD) and other diseases with similar symptoms is quite difficult to discern. Thus, hyperechogenicity of the Substantia Nigra (SN) revealed in ultrasound imaging has become a standard diagnostic marker for accurately diagnosing PD, as it is only common in PD patients. This has resulted in Transcranial B-mode Ultrasound Imaging (TCUI) becoming a widely used tactic for diagnosis of PD, as ultrasound is naturally well-suited to detect echogenicity. The accepted cutoff for hyperechogenicity is an echogenic area of 0.2cm². Currently, clinician outline the echogenic area manually with a cursor, which naturally leaves room for ambiguity and human error. Unfortunately standard B-mode images of the SN are noisy enough that determining the boundaries of the echogenic area are typically quite ambiguous. This is why we suggest the use of the Third Order Volterra Filter (ToVF), which can separate an image into its linear, quadratic, and cubic components with no spectral overlap. One common method of implementing the Volterra filter is with an adaptive Least Mean Squares (LMS) algorithm. This paper examines Zero-Attracting variants of LMS algorithms, which take advantage of the sparse nature of ultrasound data for improved performance. We found that the Zero-Attracting algorithms converged to lower steady state errors, and also performed better in terms of dynamic range and boundary definition.