In this talk, I will present new results on two-dimensional dual-tree complex wavelet transform (DTCWT) based motion magnification (MM) in the sub-pixel regime.

Motion magnification (MM) is a state-of-the-art method to magnify transverse, quasi-periodic subresolution movements of the contrast features in image sequences. The recently discovered regime of decayless kink oscillation is characterised by the low-amplitude undamped transverse oscillation of inhomogeneities such as coronal loops. Decayless oscillations are ubiquitous in the solar corona, hence a promising routine seismological diagnostics tool. Statistical studies on the decayless kink oscillation show that its averaged amplitude is ~0.17 Mm, which is 0.42 pixel in AIA spatial resolution in the EUV band. The analysis of such small motion therefore relies on MM. In this work, we examine the robustness of DTCWT-based MM in sub-pixel regime through artificial image sequences that imitates persistent kink oscillations of coronal loops with transverse profile of different transverse steepnesses. The algorithm works well on the analysis of sub-pixel oscillation, giving a linear scaling of the magnified amplitudes with the input amplitude when the magnified one is kept above 0.7 pixel. In addition, MM preserves the transverse profiles with different steepnesses. Keeping the transverse profile is important for studying any evolution of the loop, such as broadening from Kelvin-Helmholtz instability, and the consequent effect on the damping rate by resonant absorption. Thus, MM provides us with an effective and robust method for the study of low-amplitude kink oscillations of solar plasma non-uniformities and their application in coronal seismology.