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Magneto-acousto-electrical tomography (MAET), a combination of ultrasound imaging and electrical impedance tomography (EIT), offers both high resolution (in comparison to EIT) and high contrast (in comparison to ultrasound imaging). It is used to map the internal conductivity distribution of an imaging object. However, conductivity reconstruction in MAET is a challenge, so conventional MAET is mainly devoted to mapping the conductivity interface. This is primarily because integration byparts is used in the theory derivation, and the simplified measurement formula suggests the voltage is proportional to the conductivity gradient, which leads to an error in the measurement formula. In this study, the measurement signal is expressed as the convolution of acoustic velocity and conductivity distribution without using integration by parts, which retains the low-frequency term in the measurement signal. Based on the convolution formula, we subsequently propose a direct conductivity reconstruction scheme with deconvolution by utilizing the low-frequency component. We verify the proposed method based on two two-dimension models and quantify the L2 errors of reconstructed conductivity. Besides, we analyze factors influencing the reconstructed accuracy such as reconstructed regularization parameter ultrasound frequency, and noise. We also demonstrate that the spatial resolution is not influenced by the duration of excitation ultrasound. With the contributions of the proposed method, conductivity imaging appears to be feasible for application to the early diagnosis in the future.