In this paper, we propose a unified algebraic design of the generalized Moreau enhancement matrix (GME matrix) for the Linearly involved Generalized-Moreau-Enhanced (LiGME) model. The LiGME model has been established as a framework to construct linearly involved nonconvex regularizers for sparsity (or low-rank) aware estimation, where the design of GME matrix is a key to guarantee the overall convexity of the model. The proposed design is applicable to general linear operators involved in the regularizer of the LiGME model, and does not require any eigendecomposition or iterative computation. We also present an application of the LiGME model with the proposed GME matrix to a group sparsity aware least squares estimation problem. Numerical experiments demonstrate the effectiveness of the proposed GME matrix in the LiGME model.

A light field, which is equivalent to a dense set of multi-view images, has various applications such as depth estimation and 3D display. One of the essential problems in light field applications is light field interpolation, i.e., view interpolation. The interpolation accuracy is enhanced by exploiting an inherent property of a light field. One example is that an epipolar plane image (EPI), which is a 2D subset of the 4D light field, consists of many lines, and these lines have almost the same slope in a local region. This structure induces a sparse representation in the frequency domain, where most of the energy resides on a line passing through the origin. On the basis of this observation, we propose a group sparsity prior suitable for light fields to exploit their line structure fully for interpolation. Specifically, we designed the directional groups in the discrete Fourier transform (DFT) domain so that the groups can represent the concentration of the energy, and we thereby formulated an LF interpolation problem as an overlapping group lasso. We also introduce several techniques to improve the interpolation accuracy such as applying a window function, determining group weights, expanding processing blocks, and merging blocks. Our experimental results show that the proposed method can achieve better or comparable quality as compared to state-of-the-art LF interpolation methods such as convolutional neural network (CNN)-based methods.

In this paper, we propose a use of the group sparsity in adaptive learning of second-order Volterra filters for the nonlinear acoustic echo cancellation problem. The group sparsity indicates sparsity across the groups, i.e., a vector is separated into some groups, and most of groups only contain approximately zero-valued entries. First, we provide a theoretical evidence that the second-order Volterra systems tend to have the group sparsity under natural assumptions. Next, we propose an algorithm by applying the adaptive proximal forward-backward splitting method to a carefully designed cost function to exploit the group sparsity effectively. The designed cost function is the sum of the weighted group l1 norm which promotes the group sparsity and a weighted sum of squared distances to data-fidelity sets used in adaptive filtering algorithms. Finally, Numerical examples show that the proposed method outperforms a sparsity-aware algorithm in both the system-mismatch and the echo return loss enhancement.