Physics-informed neural network with coordinate inputs is susceptible to spectral bias in acoustic field reconstruction, making it difficult to accurately represent the high-frequency components of the sound field. This paper formulates acoustic field reconstruction under limited sound pressure measurement conditions as an image inpainting problem, and proposes a physics-informed neural network embedded with Fourier feature positional encoding. The proposed method not only embeds the Helmholtz equation into the loss function to enforce physical constraints, but also maps spatial coordinates into a high-dimensional feature space using sine and cosine functions of multiple frequencies, thereby effectively modulating the network′s ability to capture sound field variations across different spatial frequency scales. Simulation results demonstrate that compared with the coordinate-based physics-informed neural network method, the proposed method reduces the reconstruction error by more than 10 dB, and the number of iterations required for convergence is only 25% of that of the former. Loudspeaker experiments further validate the effectiveness of the proposed method in practical sound field reconstruction.