Image restoration via DOST and total variation regularisation

Abstract

In this study, the author proposes a total variational (TV) driven image restoration using discrete orthogonal Stockwell transform (DOST) when the noise (in the image) is an outcome of a Poisson process. Stockwell transform or S-transform (ST) is well known for its efficiency in resolving spatio-frequency components with high accuracy compared with many other transforms such as short-term Fourier transform, wavelet transform etc. This property of ST makes it more suitable for many image processing applications such as image restoration and image inpainting. By deriving the objective function and constraints of the optimisation problem (image restoration problem) based on the ST coefficients, the model becomes more robust in terms of preserving high resolution in the spatio-frequency domain. Images are modelled as an outcome of a Poisson process in many medical and telescopic imaging applications. The Poisson noise corruption is mainly due to the lack of a sufficient number of photons to reconstruct the data. In this study, corrupted images are restored due to the Poisson process (by which the data is formed) using the DOST under a non-local TV framework. The model is analysed and compared with the state-of-the-art Poisson noise removal methods using visual and statistical measures.