基于lp范数的压缩感知图像重建算法研究

图像重建是光学成像、光声成像、声纳成像、核磁共振成像、 天体成像等物理成像领域中的关键技术之一. 近年来提出的压缩感知理论指出: 对稀疏或者可压缩信号进行少量非自适应线性投影,投影信号含有足够的信息, 从而能对信号进行高概率重建. 压缩感知已被应用于多种物理成像系统. 将罚函数法和修正Hesse阵序列二次规划方法相结合, 并采用了分块压缩感知思想, 提出一种基于l_p范数的压缩感知图像重建算法. 以cameraman, barbara和mandrill图像为例, 采用该算法进行图像重建. 首先, 在不同采样率下对图像重建. 即便采样率低至0.3时, 也能获得高达32.23dB的信噪比, 重建图像清晰可辨. 验证了该算法的正确性. 其次, 将该算法与正交匹配追踪算法进行对比, 在采样率达到0.5以上时, 能够获得高信噪比的重建图像, 成像时间也大为减少, 特别是采样率为0.7时, 成像时间减少88%. 最后, 与现有基于l_p 范数的压缩感知图像重建算法进行对比, 计算结果表明在成像质量有所提高的基础上, 成像时间大为缩短. 关键词： 图像重建 压缩感知 罚函数 修正Hesse阵序列二次规划

An algorithm for image reconstruction based on lp norm

Image reconstruction is one of the key technologies in the fields of physical imaging, which include optical imaging, photoacoustic imaging, sonar imaging, magnetic resonance imaging, and celestial imaging etc. Compressive sensing theory, the new research spot in recent years, describes that a small group of non-adaptive linear projections of a sparse or compressible signal contains enough information for signal reconstruction. Compressive sensing has been applied in many physical imaging systems. In this paper, we propose a new image reconstruction algorithm based on l_p norm compressive sensing by combining the penalty function and revised Hesse sequence quadratic programming, and using block compressive sensing. Several images, such as “cameraman”, “barbara” and “mandrill”, are chosen as the images for image reconstruction. First, we take different sampling rates for image reconstruction to verify the algorithm. When the sampling rate is as low as 0.3, the signal-to-noise ratio of the reconstructed image can reach up to 32.23 dB. Then, when the sampling rate is above 0.5, by comparing with OMP algorithm, reconstructed images can be obtained with a higher signal-to-noise ratio and a shorter imaging time. Especially, when the sampling rate is 0.7, the imaging time is reduced by 88%. Finally compared with the existing algorithm based on l_p norm compressive sensing, simulation results show that the new algorithm can improve the signal-to-noise ratio of reconstructed images, and greatly reduce the imaging time.
Keywords： image reconstruction compressive sensing penalty function revised Hesse sequence quadratic programming