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Compressive imaging is an imaging way based on the compressive sensing theory, which could achieve to capture the high resolution image through a small set of measurements. As the core of the compressive imaging, the design of the measurement matrix is sufficient to ensure that the image can be recovered from the measurements. Due to the fast computing capacity and the characteristic of easy hardware implementation, The Toeplitz block circulant matrix is proposed to realize the encoded samples. The measurement matrix is usually optimized for improving the image reconstruction quality. However, the existing optimization methods can destroy the matrix structure easily when applied to the Toeplitz block circulant matrix optimization process, and the deterministic iterative processes of them are inflexible, because of requiring the task optimized to need to satisfy some certain mathematical property. To overcome this problem, a novel method of optimizing the Toeplitz block circulant matrix based on the particle swarm optimization intelligent algorithm is proposed in this paper. The objective function is established by the way of approaching the target matrix that is the Gram matrix truncated by the Welch threshold. The optimized object is the vector composed by the free entries instead of the Gram matrix. The experimental results indicate that the Toeplitz block circulant measurement matrix can be optimized while preserving the matrix structure by our method, and result in the reconstruction quality improvement.
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