In this paper, an economical and effective soft pressure sensor for underwater sea lamprey detection is proposed, which consists of an array of piezoresistive elements between two layers of perpendicular copper tape electrodes, forming a passive resistor network. With multiplexers, the apparent resistance corresponding to each pixel of the sensing matrix can be measured directly, where the pixel is identified with the row and the column of the respective electrodes. However, this measured two-point resistance is not equal to the actual cell resistance for that pixel due to the crosstalk effect in the resistor network. Since the cell resistance reflects directly the pressure applied on each pixel, the relationship between the cell resistance and the measured two-point resistance is analyzed for a passive matrix of any size. More importantly, several regularized least-squares algorithms are proposed to reconstruct the cell resistance profile from the two-point resistance measurements, with enhanced robustness of the reconstruction in the presence of measurement noises and modeling errors. The proposed pressure sensor is applied to detect the suction attachment of sea lampreys, a devastating invasive species in the Great Lakes region. Experimental results demonstrate that the pressure sensor can successfully capture the rim profile of the lamprey’s sucking mouth. Moreover, the performance and computational complexity of the reconstruction algorithms with different regularization functions are compared.