This paper examines two fundamental challenges in two areas, respectively, which have been intensively researched in the field of image processing and communications, i.e., digital picture coding/ compression and digital picture (including both video and still images) restoration (or de-noising). It reflects on historical developments and reviews the state-of-theart in the area of digital picture coding. Quantitative perceptual distortion measure based on the human visual system is identified as the weakest link in the current picture coding framework and remains a fundamental challenge in devising the next generation picture coding systems. In the area of picture restoration, the paper takes a special interest in surveillance and security video/image de-noising task for forensic investigations. Highlighting the most recent advances and the inadequacies in existing image de-noising techniques, it focuses on a fundamental challenge in designing a unified picture de-noising framework, including noise modeling, for removal of analogue and digital surveillance video distortions. 1