The recently introduced Compressed Sensing (CS) theory explains how sparse or compressible signals can be reconstructed from far fewer samples than what was previously believed possible. The CS theory has attracted significant attention for applications such as Magnetic Resonance Imaging (MRI) where long acquisition times have been problematic. This is especially true for dynamic MRI applications where high spatio-temporal resolution is needed. For example, in cardiac cine MRI, it is desirable to acquire the whole cardiac volume within a single breath-hold in order to avoid artifacts due to respiratory motion. Conventional MRI techniques do not allow reconstruction of high resolution image sequences from such limited amount of data. Vaswani et al. recently proposed an extension of the CS framework to problems with partially known support (i.e. sparsity pattern). In their work, the problem of recursive reconstruction of time sequences of sparse signals was considered. Under the assumption that the support of the signal changes slowly over time, they proposed using the support of the previous frame as the "known" part of the support for the current frame. While this approach works well for image sequences with little or no motion, motion causes significant change in support between adjacent frames. In this paper, we illustrate how motion estimation and compensation techniques can be used to reconstruct more accurate estimates of support for image sequences with substantial motion (such as cardiac MRI). Experimental results using phantoms as well as real MRI data sets illustrate the improved performance of the proposed technique.