Histopathological images show a vital role in lung cancer detection. The acquisition of histopathological images is commonly affected by Poisson noise, artifact and distortion. These issues can significantly degrade image quality, making it challenging for doctors and radiologists to interpret them accurately. In this paper, a modified fourth-order partial differential equation with maximum likelihood estimation is proposed to address these issues. Unlike traditional fourth-order partial differential equation filtering, a restoration property is added to preserve the edges and fine details of the image. The effectiveness of the proposed method is judged on lung and colon cancer histopathological image dataset i.e., LC25000 in terms of visual as well as numerical calculation. Apart from this, a comparative study has been also presented with respect to the existing methodologies. The perceptual and numerical outcomes of proposed method outperform the existing methodologies. Furthermore, it shows that it is a good for the removal of Poisson noise.