一种改进的稀疏信号重构的梯度投影算法

Abstract

压缩感知理论作为一种全新的信号采集、编解码理论，已被广泛地应用于图像处理、模式识别、自动控制和生物传感等领域，并展现出强大的力量。为了更快速地求解压缩感知问题，在稀疏信号重构的Barzilai-Borwein (B-B)梯度投影(Barzilai-Borwein Gradient Projection for Sparse Reconstruction, GPSR-BB)算法的基础上，采用预测校正的技巧，提出了一种改进的梯度投影算法。该算法首先由常数步长的梯度投影产生一个预测点，再根据预测点及B-B方法计算步长得到新的迭代点。新算法单步迭代计算同样简单，且采用预测校正技巧可使迭代点更接近问题的解，从而可望减少算法的总的迭代次数。对随机生成的测试问题进行数值实验，数值结果表明新算法的运行时间要少于GPSR-BB算法。 As a novel sampling, coding and decoding theory, compressed sensing has been a powerful tool which was widely used to the fields of image processing, pattern recognition, automatic control, biological sensors and so on. Based on the Barzilai-Borwein (B-B) gradient projection for sparse reconstruction (GPSR-BB), this paper proposed a new algorithm by using predictor-corrector technique for solving compressed sensing problem fast. In the new algorithm, a predicted point was first generated by traditional gradient projection and then a new iteration point was obtained with B-B method according to the predicted point. In our algorithm, the calculation of a single iteration is also simple, and by using predictor-corrector technique, the iteration point may be closer to the solution of the problem, thereby the number of the iteration would be reduced. Numerical results show that the running time of the new algorithm is less than GPSR-BB for some randomly generated test problems.