一种优化恢复压缩传感矩阵的模糊自适应方法

Fuzzy adaptive method for optimizing recovery of compressive sensing matrix

为了解决高维信号恢复过程中的欠定线性问题,该文提出一种优化恢复压缩传感矩阵的模糊自适应方法并应用在图像重建和识别中。首先对输入样本通过局部分块并建立三阶张量的样本描述方式,提出对降维信号进行多尺度结构分析和独立成分分析,并对结果执行压缩观测,从而使线性观测之间保持线状奇异性和统计独立性。提出一种优化传感矩阵的模糊代价函数,使传感矩阵的原子更新随后按照模糊方式计算,优化后的观测矩阵与字典矩阵之间保持了低相干性。该文方法使样本的稀疏信号在相同重构条件下具备了更优的测量数目和质量。在ORL和Yale人脸数据库及91幅自然图像库上的实验结果验证了本文算法的有效性。

To solve the underdetermined linear problem in the signal recovery from high-dimensional data,a fuzzy adaptive method for optimizing recovery of compressive sensing matrix is proposed for image reconstruction and recognition.By this means,each high dimensional input sample is firstly partitioned into the several local blocks,and those local blocks are combined to represent the sample as a third-order tensor.Moreover,the compressive measurement is performed on the dimensionality-reduced source signal,which is able to find the properties of statistical independence and linear singular by using multi-scale structural analysis and independent component analysis.Finally,a new fuzzy cost function for optimization of sensing matrix is proposed,in which the update of atoms from sensing matrix are fuzzily handled,and the low coherence is obtained between the properties of observation matrix and dictionary matrix.The merit of the method is that the sparse signal has desirable properties for the number of measurements and representation qualities under the same reconstruction conditions.Extensive experimental studies conducted on ORL,Yale face images and 91 natural images databases show that the effectiveness of the proposed method.