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This paper deals with an image colorization and proposes a new image colorization algorithm. Assuming that the difference of color values between neighbor pixels is given as a monotonically increasing function of the difference of grayscale values between neighbor pixels, a colorization function is proposed, and the colorization problem is formulated as the weighted least squares problem using this function. In order to reduce the dependence on the value of a parameter in the algorithm, this paper utilizes a finite series approximation and provides a fast colorization algorithm. Numerical examples show that the proposed algorithm colorizes a grayscale image efficiently.

This paper proposes a new image colorization algorithm based on the mixed l 0 /l 1 norm minimization. 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 l 0 /l 1 norm minimization, which is solved approximately by an iterative reweighted least squares (IRLS) algorithm. Numerical examples show that the proposed algorithm colorizes a grayscale image well using a small number of color pixels.

SUMMARYThis 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.

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SUMMARYThis 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 p / 1 norm minimization. Introducing some assumptions, this paper formulates the super-resolution problem as a mixed 0 / 1 norm minimization and relaxes the 0 norm term to the p 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 paper proposes a representative pixel (RP) extraction algorithm and chrominance image recovery algorithm for the colorization-based digital image coding. The colorization-based coding methods reduce the color information of an image and achieve higher compression ratio than JPEG coding; however, they take much more computing time. In order to achieve low computational cost, this paper proposes the algorithm using the set of multiple-resolution images obtained by colorization error minimizing method. This algorithm extracts RPs from each resolution image and colorizes each resolution image utilizing a lower resolution color image, which leads to the reduction of the number of RPs and computing time. Numerical examples show that the proposed algorithm extracts the RPs and recovers the color image fast and effectively.