Linear Projection for Transducer Position Calibration and Crosstalk Detection in Low-SNR USCT Systems

3D ultrasound computed tomography (3D USCT) requires precise transducer positioning and knowledge of the background speed of sound (SoS). However, factors such as channel-to-channel variability introduced by multiplexer switching, temperature-induced SoS drift, and mechanical misalignment degrade image quality in large apertures. We present a robust linear projection method that operates below the noise level and can detect crosstalk. With spherical back-projection, all A-scans are linearly processed and matched-filtered, then projected into a three-dimensional spatial domain without explicit time-of-flight (ToF) picking. The resulting 3D response maps the origin (emitter) or sink (receiver) of the wave in a linear, pseudo-probabilistic representation, enabling separate examination of transmit and receive paths and isolation of hardware effects. Multiple maxima can be associated with distinct sources such as electrical crosstalk. On a prototype system, 82.4 % of transducers matched expected positions (median deviation ≈1 mm); six transducer-array systems were detected as rotated by 118^◦, later confirmed mechanically. The method provides robust system analysis, fault detection, and additional system-health information for low-SNR arrays.