Due to the long aperture, the high-resolution imaging for strip-map SAR with missing data is a challenge, in which the range migration correction and phase error correction are challenging. In this paper, a high-resolution imaging method of this type of data based on compressed sensing (CS) is proposed, which divides the strip-map data into several sub-apertures restored by CS and recombined to the strip-map data. The basis matrix and the measurement matrix for CS are deduced. The sub-aperture data is autofocused by the Projection Approximation Subspace Tracking (PAST) algorithm to meet the sparse requirement for the reconstructed image and the intact phase error data is restored by CS in order to combine the subapertures. A high-resolution image of the restored data can be obtained by conventional imaging method which performs range migration and autofocus. INDEX TERMS Synthetic aperture radar, compressed sensing, PAST algorithm, missing data, highresolution imaging.

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