## 1 Introduction  
Multi-channel ultrasound measurements allow a high level of flexibility in the data acquisition of imaging and defect recognition. A common acquisition scheme is the full matrix capture (FMC), which denotes consecutively transmitting with one transducer element after another, while all elements receive on each cycle. This acquisition scheme is then commonly paired with the Total Focusing Method (TFM) [1], which is an imaging algorithm applied in post-processing. When being applied for inline inspection, where speed is crucial, FMC measurements suffer from a higher acquisition time compared to, e.g., a transmit-focused beam, as each measurement cycle requires sending with each array element. The purpose of this study is to derive a simple heuristic for choosing only a subset of the elements for transmission to improve the acquisition speed while preserving the achievable imaging quality. The algorithm takes a priori knowledge of the problem geometry, i.e., a forward model, into account. Furthermore, only a specific region of interest is considered, limiting the width of the usable aperture. In the literature, reducing the number of transmit or receive channels of a FMC acquisition has been studied both in the light of reducing acquisition as well as processing times and hardware cost. The design of such sparse ultrasound arrays is extensively being studied for medical applications, where the most common optimization criteria are side lobe levels and point spread functions over the full aperture. In non-destructive testing, transmit subsampling is being investigated in [2], where the authors show that using two or four elements near the end of the array for excitation is to be favored over transmitting with all elements as one. In [3, 4], equispaced element choices as well as using only the outer elements are being investigated, with the conclusion that using fewer elements can be an application-dependent choice to improve measurement speed. In [5], sparse arrays are designed using a combination of almost different sets and a genetic algorithm using attributes of the point spread function as the fitness measure. In [6], using fewer receivers is investigated for near surface defects. In [7], particle swarm optimization is performed to reduce the computation time of FMC by using fewer elements. In [8], a Compressive Sensing (CS)-based approach is used for reducing the data both in receive as well as in frequency based on Cramer Rao Bounds. All aforementioned publications deal with the optimization of the patterns in terms of the full aperture width. In contrast, we consider a scenario where, due to the limited extent of the region of interest, only a subset of the full width of the aperture is of relevance. Similar investigations were carried out in [9] for acoustic source localization using microphones, prioritizing certain regions in the image. In the same spirit, we derive a simpler heuristic. In contrast, our approach is based on a more sophisticated forward model, including effects such as refraction and beam patterns, for an application in non-destructive testing. We investigate a scenario where a bowed transducer array is positioned over a moving pipe in production. While the transducer encloses a section of the pipe to ensure recording echoes from a large variety of angles, as well as to enable in-field adjustability, the region where defects are expected is limited to the weld. This also limits the usable aperture, posing the question of how to choose the active array elements. Consequently, we derive a scheme where the transmit elements are chosen on the basis of the a priori knowledge of the problem geometry and area of interest. The reconstruction as well as the array element selection are performed on the basis of a linearized forward model, which, calculated by a raycasting scheme, incorporates effects as transducer directivity and refraction at the pipe boundary. The reconstruction is performed by TFM.