A New Random Sampling Method based on Compressed Sensing

One of the key requirements in compressed sensing theory is use of the random undersampling method, which renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, pure random undersampling does not provide such a control. Jittered-undersampling scheme remedies this lack of control. However, the size of the maximum gap is related to the undersampling factor, when the undersampling factor is small, the control of the maximum gap is too strict. This paper presents a new spatial random sampling method which can be used to control the maximum gap size flexibly.