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提出了一种通过求解L1范数最小化问题来重建四元数信号的算法,并且同时考虑了有噪声和没有噪声2种应用场景.该算法首先将四元数域的L1范数最小化问题转化为实数域的二次锥规划问题,然后通过工具包如SeDuMi来解决这个二次锥规划问题.为了验证所提出算法的正确性和有效性,进行了相关的数值试验.试验结果表明:在没有噪声的情况下,在某些实际可接受的条件下原始信号的精确重建是可以实现的;在有噪声的情况下,所提出的算法对于测量中的加性噪声具有鲁棒性.该算法可以被应用于四元数域基于压缩感知理论的信号重建中.
An algorithm for reconstructing quaternion signals by solving the L1 norm minimization problem is proposed, and two applications of noises and noises are considered simultaneously.The algorithm firstly reduces the L1 norm of the quaternion field And then solve the quadratic conic programming problem through a toolkit such as SeDuMi.In order to verify the correctness and validity of the proposed algorithm, a numerical experiment has been carried out.The experimental results show that in the Without noise, the exact reconstruction of the original signal is achievable under some practical conditions; the proposed algorithm is robust to the additive noise in the measurement under noisy conditions. The algorithm It can be used in signal reconstruction of quaternion field based on compressive sensing theory.