Abstract In this paper, quantum digital image processing algorithms based on quantum measurement are proposed, which consist of quantum image edge detection algorithm and quantum adaptive median filtering algorithm. These algorithms follow the quantum signal algorithm framework: First, the pixel of input image is transformed into qubit state representation. In this process, a pixel is transformed into single qubit state representation in quantum image edge detection algorithm, while in quantum adaptive median filtering algorithm a pixel is transformed into dual qubits state representation. Dual qubits state has four basis vectors, which can reflect more information of the represented pixel. Thus the represented pixel can be manipulated more accurately. Second, the quantum measurement outcomes are obtained based on quantum measurement postulate. Third, the quantum measurement outcomes are transformed into the algorithm outcomes. In the final part, experiments are performed to compare our method with conventional methods.