Crawling wave sonoelastography enables the measurement of viscoelastic properties of soft tissue. Recently, the dominant component analysis AM-FM method was proposed for modeling non-stationary patterns in crawling wave sonoelastography to locally estimate their shear wave speed. Although evaluations show consistent results for homogeneous and inhomogeneous phantoms, high noise levels and few available data samples do not allow a rigorous spectral analysis by using a filterbank. We propose a novel method to isolate AM-FM components based on the null space pursuit algorithm that alleviates such limitations. Preliminary results for the proposed method for homogeneous and inhomogeneous phantoms, and a comparison to alternative methods are presented.