Compressed sensing (CS) multi‐camera network reconstruction has attracted much attention in the field of distributed CS networks. However, many multi‐camera network reconstructions based on CS usually recover every image separately; the view's dependency and geometrical structure among these multi‐view images could be rarely considered in this way, which will result in some unsatisfied joint reconstruction results. Here, the authors introduce to extract the multiple view geometry from multi‐view images to construct the view's dependency observation model. Based on the proposed parametric transformation observation model, they propose a novel CS joint reconstruction method of multi‐view image that guided by the spatial correlation and low‐rank background constraints. The eventual optimisation model could be relaxed to a series of convex optimisation problems, which could be efficiently solved by combining the variable splitting and alternate iteration technique. The extended experimental results indicate that they proposed method has achieved a remarkable improvement in both objective criterion and visual fidelity compared with other competitive reconstruction methods.

Feature selection aims to select a subset of features from high-dimensional data according to a predefined selecting criterion. Sparse learning has been proven to be a powerful technique in feature selection. Sparse regularizer, as a key component of sparse learning, has been studied for several years. Although convex regularizers have been used in many works, there are some cases where nonconvex regularizers outperform convex regularizers. To make the process of selecting relevant features more effective, we propose a novel nonconvex sparse metric on matrices as the sparsity regularization in this paper. The new nonconvex regularizer could be written as the difference of the $\ell _{2,1}$ norm and the Frobenius ( $\ell _{2,2}$ ) norm, which is named the $\ell _{2,1-2}$ . To find the solution of the resulting nonconvex formula, we design an iterative algorithm in the framework of ConCave-Convex Procedure (CCCP) and prove its strong global convergence. An adopted alternating direction method of multipliers is embedded to solve the sequence of convex subproblems in CCCP efficiently. Using the scaled cluster indictors of data points as pseudolabels, we also apply $\ell _{2,1-2}$ to the unsupervised case. To the best of our knowledge, it is the first work considering nonconvex regularization for matrices in the unsupervised learning scenario. Numerical experiments are performed on real-world data sets to demonstrate the effectiveness of the proposed method.