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This paper is concerned with partial differential equation (PDE)-based image denoising for random-valued impulse noise. We introduce the notion of ENI (the abbreviation for “edge pixels, noisy pixels, and interior pixels”) that denotes the number of homogeneous pixels in a local neighborhood and is significantly different for edge pixels, noisy pixels, and interior pixels. We redefine the controlling speed function and the controlling fidelity function to depend on ENI. According to our two controlling functions, the diffusion and fidelity process at edge pixels, noisy pixels, and interior pixels can be selectively carried out. Furthermore, a class of second-order improved and edge-preserving PDE denoising models is proposed based on the two new controlling functions in order to deal with random-valued impulse noise reliably. We demonstrate the performance of the proposed PDEs via application to five standard test images, corrupted by random-valued impulse noise with various noise levels and comparison with the related second-order PDE models and the other special filtering methods for random-valued impulse noise. Our two controlling functions are extended to automatically other PDE models.