Sub-Nyquist radar is an analog-to-information based radar system with the assumption of sparse echo signals. We study the reconstruction of moving target echoes obtained from the sub-Nyquist radar. Different from the reconstruction of echo signals from a single pulse

the moving targets may be across range cells in a coherent processing interval and thus the echo signals have the property of the time-varying sparsity. However

it has been found that the sparse positions obey a probabilistic distribution and then a random model is adopted to describe the sparsity. The reconstruction of the multiple echoes is transformed into a weighted sparse reconstruction problem. An orthogonal-projection-based weighted sparse segment-sliding reconstruction (OP-WSegSR) scheme is proposed in this paper. Utilizing the estimation of sparse positions in the previous pulse

the scheme projects the measurements of the current segment onto the orthogonal complement subspace spanned by the interference generated in the segmentation process and then the adjacent interference is greatly rejected. Simulations show the effectiveness of the OP-WSegSR scheme.