一种改进的变步长前后向追踪重建算法

压缩感知中前后向追踪（forward-backward pursuit，FBP）算法能有效缩短重建时间，但一旦迭代过程中前向、后向步长确定，将导致计算时间增长，影响重构效率，因此，提出一种改进的FBP算法，称为变步长前后向追踪算法（variable step size forward-backward pursuit，VSSFBP）.该算法引入判决阈值和等比因子，考虑到估计的稀疏度远小于真实稀疏度，选择较大迭代步长，减少迭代次数，缩短运行时间；同时考虑到当估计的稀疏度达到一定值时，减小迭代步长，减慢逼近的速度，提高信号重构精度.仿真结果表明：VSSFBP算法在保证重构效果的同时，明显缩短了重构时间.当图像压缩比为0.45时，信噪比提高了1 dB，峰值信噪比提高了0.8 dB，重构时间降低为原来FBP算法的42.04%.与同类算法相比，在保持较高的峰值信噪比和信噪比的条件下， VSSFBP算法消耗的时间大大缩短，重构速度更快，重构信号更精确.

An Improved Variable Step Size Forward-Backward Pursuit Algorithm in Compressive Sensing

There is a forward-backward pursuit（FBP） algorithm in the compressed sensing（CS） which can efficiently decrease framing time. However once forward step and backward step were determined during iteration , computing time would increase and framing efficiency would be affected. In this paper , an improved variable step size forward-backward pursuit （VSSFBP） algorithm was proposed. By integrating the ideas of double thresholds and variable step size, the proposed algorithm could decrease the computation time and control the accuracy of reconstruction without knowledge about the sparsity of the signal. And because the estimated sparsity is smaller than the true sparsity , larger iteration step was chosen to reduce the number of iterations to shorting the running time. Simultaneously considering unknown sparsity, iteration step was reduced and approaching speed was slowed down to improve the accuracy of sig-nal reconstruction. The simulation results showed that the proposed algorithm can reduce the iteration times with better reconstruction performances. When the compression ratio of the object is 0.45, this algorithm has 1 dB gain in the sig-nal-to-noise ratio and 0.8 dB gain in the peak signal-to-noise ratio over FBP algorithm , and the reconstruction time is only 42.04% of FBP algorithm. In a word, keeping in higher PSNR and SNR, VSSFBP algorithm has greatly re-duced time-consuming and increased reconstruction speed compared with other algorithms. Simultaneously the algo-rithm makes reconstructed signal more precise, so the prospect of it′s application is very broad.