This letter proposes a new image colorization algorithm based on the sparse optimization. Introducing some assumptions, a problem of recovering a color image from a grayscale image with the small number of known color pixels is formulated as a mixed l0/l1 norm minimization, and an iterative reweighted least squares (IRLS) algorithm is proposed. Numerical examples show that the proposed algorithm colorizes the grayscale image efficiently.

This letter proposes a simple heuristic to identify the discrete-time switched autoregressive exogenous (SARX) systems. The goal of the identification is to identify the switching sequence and the system parameters of all submodels simultaneously. In this letter the SARX system identification problem is formulated as the l0 norm minimization problem, and an iterative algorithm is proposed by applying the reweighted least squares technique. Although the proposed algorithm is heuristic, the numerical examples show its efficiency and robustness for noise.

This paper proposes an image inpainting algorithm based on multiple linear models and matrix rank minimization. Several inpainting algorithms have been previously proposed based on the assumption that an image can be modeled using autoregressive (AR) models. However, these algorithms perform poorly when applied to natural photographs because they assume that an image is modeled by a position-invariant linear model with a fixed model order. In order to improve inpainting quality, this work introduces a multiple AR model and proposes an image inpainting algorithm based on multiple matrix rank minimization with sparse regularization. In doing so, a practical algorithm is provided based on the iterative partial matrix shrinkage algorithm, with numerical examples showing the effectiveness of the proposed algorithm.

This letter deals with a sparse signal recovery problem and proposes a new algorithm based on the iterative reweighted least squares (IRLS) algorithm. We assume that the non-zero values of a sparse signal is always greater than a given constant and modify the IRLS algorithm to satisfy this assumption. Numerical results show that the proposed algorithm recovers a sparse vector efficiently.

This paper deals with the problem of reconstructing a high-resolution digital image from a single low-resolution digital image and proposes a new intra-frame super-resolution algorithm based on the mixed lp/l1 norm minimization. Introducing some assumptions, this paper formulates the super-resolution problem as a mixed l0/l1 norm minimization and relaxes the l0 norm term to the lp norm to avoid ill-posedness. A heuristic iterative algorithm is proposed based on the iterative reweighted least squares (IRLS). Numerical examples show that the proposed algorithm achieves super-resolution efficiently.

This letter deals with the signal declipping algorithm based on the matrix rank minimization approach, which can be applied to the signal restoration in linear systems. We focus on the null space of a low-rank matrix and provide a block adaptive algorithm of the matrix rank minimization approach to signal declipping based on the null space alternating optimization (NSAO) algorithm. Numerical examples show that the proposed algorithm is faster and has better performance than other algorithms.

This letter deals with a system identification problem with unknown model order, which can be formulated as the matrix rank minimization problem by applying the subspace identification method. A sequential rank minimization algorithm is provided by modifying the null space based alternating optimization (NSAO) algorithm, and a model order identification algorithm is proposed. Numerical examples show that the proposed sequential algorithm can adaptively identify the model order of switched systems whose model order changes.

This letter deals with an audio declipping problem and proposes a multiple matrix rank minimization approach. We assume that short-time audio signals satisfy the autoregressive (AR) model and formulate the declipping problem as a multiple matrix rank minimization problem. To solve this problem, an iterative algorithm is provided based on the iterative partial matrix shrinkage (IPMS) algorithm. Numerical examples show its efficiency.