Ultrasonic array imaging is used in nondestructive testing for the detection and characterization of defects. The scattering behavior of any feature can be described by a matrix of scattering coefficients, called the scattering matrix. This information is used for characterization, and contrary to image-based analysis, the scattering matrix allows the characterization of defects at the subwavelength scale. However, the defect scattering coefficients are, in practice, contaminated by other nearby scatterers or significant structural noise. In this context, an optimal procedure to extract scattering features from a selected region of interest in a beamformed image is here investigated. This work proposes two main strategies to isolate a target scatterer in order to recover exclusively the time responses of the desired scatterer. In this article, such strategies are implemented in delay-and-sum and frequency-wavenumber forms and optimized to maximize the extraction rate. An experimental case in a polycrystalline material shows that the suggested procedures provide a rich frequency spectrum of the scattering matrix and are readily suited to minimize the effects of surrounding scattering noise. In doing so, the ability to deploy imaging methods that rely on the scattering matrix is enabled.