Image sensors with internal computing capability enable in-sensor computing that can significantly reduce the communication latency and power consumption for machine vision in distributed systems and robotics. Two-dimensional semiconductors have many advantages in realizing such intelligent vision sensors because of their tunable electrical and optical properties and amenability for heterogeneous integration. Here, we report a multifunctional infrared image sensor based on an array of black phosphorous programmable phototransistors (bP-PPT). By controlling the stored charges in the gate dielectric layers electrically and optically, the bP-PPT's electrical conductance and photoresponsivity can be locally or remotely programmed with 5-bit precision to implement an in-sensor convolutional neural network (CNN). The sensor array can receive optical images transmitted over a broad spectral range in the infrared and perform inference computation to process and recognize the images with 92% accuracy. The demonstrated bP image sensor array can be scaled up to build a more complex vision-sensory neural network, which will find many promising applications for distributed and remote multispectral sensing.