A study on staircase artefacts in total variation image restoration

The total variation (TV) regularization is used in various image processing domains such as image super-resolution, reconstruction, compressed sensing, and restoration mainly due to its edge-preserving capabilities. However, the main problem when using the TV regularization is the staircase artifacts. For image restoration, the staircase artifacts manifest themselves by producing a smeared and blocky restored image, especially when the noise level is high. This problem has been a long-standing problem, and various improvements to TV regularization have been proposed. This paper studies the effects of the staircase artifacts produced by two different noises; Gaussian noise and salt-and-pepper noise. For this purpose, we compare three well-known algorithms, the alternating direction method of multipliers (ADMM), alternating minimization (AM), and accelerated AM, and observe the effects of staircase artifacts produced between the three algorithms. As a by-product, the accelerated AM tested for the salt-and-pepper noise can be seen as a new extension of the existing accelerated AM method. Results show that it is interesting to study further the effects of different types of noise and the algorithms to mitigate the staircase artifacts produced.