稀疏表示中稀疏系数的l-1范数的特性分析

稀疏表示模型被广泛应用于计算机视觉和模式识别领域,该数学模型中参数稀疏系数的l-1范数作为图像块的活跃度度量(activity level measurement,ALM)特征被成功应用于稀疏表示图像融合领域,但该参数的物理意义至今没有明确的解释。以此问题为出发点,首先,从广义的角度出发,将图像块的稀疏系数向量的l-1范数定义为奇异度;其次,在理论上定性说明了该定义的合理性;第三,通过实验,以图形化方式侧面展示了该参数的物理意义。理论与实验分析结果表明:信号向量的稀疏系数可看作该向量在字典基函数下的投影坐标,稀疏系数的l-1范数可用来描述信号的奇异性特征。

Characteristic analysis for thel-1norm of sparse coefficients in sparse representation

The sparse representation model is widely used in the field of computer vision and pattern recognition. The l-1 norm of sparse coefficients in this model is successfully applied in the field of sparse representation-based image fusion as an activity level measurement (ALM) feature of image patches, but the physical meaning of this parameter is not clearly explained so far. Starting from this issue, firstly, from a generalized viewpoint, thel-1norm of the sparse coefficient vector of an image patch is defined as the singularity; secondly, the rationality of the definition is qualitatively explained in theory; thirdly, the physical meaning of the parameter is shown in a graphical way through experiments. Theoretical and experimental analysis results show that the sparse coefficient of the signal vector can be regarded as the projection coordinate of the signal under the dictionary basis function, and thel-1 norm of the sparse coefficient can be used to describe the singularity characteristics of a signal.