# remove spatial sinusoid noise from 2d image

Given a 2D image where each row of pixels is shifted by some amount horizontally in a sinusoid fashion, is it possible to recover the original image?

Imagine a camera that can capture one row at a time, and is moved vertically to capture the whole image. While it is moved, the camera vibrates, resulting in noise similar to above picture.

If there is a known reference object that spans the entire height of the picture, such as a vertical bar, this is simple enough to solve. But can you detect and correct this sort of noise if there is no fixed object in the picture?

If that is not possible, what if you assume some limits for the noise: the approximate amplitude and frequency can be known, but not the phase. Is there a solution under these constraints?

• $l_{1}$ norm minimization in some transform basis.