Katsumi Konishi

A Nuclear Norm Heuristic Approach to Fractionally Spaced Blind Channel Equalization

This letter proposes an algorithm for the blind fractionally spaced equalization (FSE). We show that the rank minimization approach leads to the reduction of degrees of freedom in the blind FSE problem and improves the quality of equalization. By introducing the nuclear norm heuristic, the design problem of blind channel equalization is formulated as the nuclear norm minimization problem. We also show that the effect of noise is reduced by minimizing the nuclear norm. Numerical examples demonstrate the effectiveness of the proposed algorithm.

Fast communication: Iterative partial matrix shrinkage algorithm for matrix rank minimization

This paper proposes a new matrix shrinkage algorithm for matrix rank minimization problems. The proposed algorithm provides a low rank solution by estimating a matrix rank and shrinking non-dominant singular values iteratively. We study the convergence properties of the algorithm, which indicate that the algorithm gives approximate low-rank solutions. Numerical results show that the proposed algorithm works efficiently for hard problems with low computing time.

Parallel GPU implementation of null space based alternating optimization algorithm for large-scale matrix rank minimization

This paper provides an alternating optimization algorithm for large-scale matrix rank minimization problems and its parallel implementation on GPU. The matrix rank minimization problem has a lot of important applications in signal processing, and several useful algorithms have been proposed. However most algorithms cannot be applied to a large-scale problem because of high computational cost. This paper proposes a null space based algorithm, which provides a low-rank solution without computing inverse matrix nor singular value decomposition. The algorithm can be parallelized easily without any approximation and can be applied to a large-scale problem. Numerical examples show that the algorithm provides a low-rank solution efficiently and can be speed up by parallel GPU computing.

Rank minimization approach to image inpainting using null space based alternating optimization

This paper proposes a novel image inpainting based on the matrix rank minimization. Assuming that an image can be modeled by the autoregressive (AR) model, this paper formulates the image inpainting problem as the signal recovery problem of an AR model. The main result of this paper is to reformulate this problem as the matrix rank minimization and to provide an inpainting algorithm based on the null space based alternating optimization (NSAO) algorithm. Numerical examples show that the proposed algorithm recovers missing pixels efficiently.

Image colorization algorithm using series approximated sparse function

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.

Structured matrix rank minimization approach to image inpainting

This paper proposes a structured matrix rank minimization approach to a novel image inpainting. We utilize the autoregressive (AR) model to describe the gray level of image, and formulate the image inpainting problem as the signal recovery problem by estimating the model order. This problem is described as the rank minimization problem, which is NP hard in general. To solve the problem approximately, this paper proposes an algorithm utilizing the null space based alternating optimization (NSAO) algorithm. Numerical examples show that the proposed algorithm recovers missing pixels well.

Image colorization based on the mixed l 0 /l 1 norm minimization

This paper proposes a new image colorization algorithm based on the mixed L0/L1 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 L0/L1 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.

An image colorization algorithm using sparse optimization

This paper proposes a new digital image colorization algorithm using the sparse optimization. We deal with the colorization problem where a grayscale image is colorized using a full color image with a similar composition, and formulate this problem as the sparse optimization problem. We also provide an iterative reweighted least squares (IRLS) algorithm to solve this problem approximately, and the full color image is obtained in practical time. Numerical examples show that the proposed algorithm colorizes a grayscale image well.

Optimal Task Scheduling Algorithm for Parallel Processing

This paper proposes an optimal task scheduling algorithm for parallel processing. The scheduling problem is formulated as a 0-1 integer problem, where a priority of processing is represented by constraints of the problem. A numerical example shows the effectiveness of the proposing scheduling.

A system identification method with roughly quantized data using semidefinite programming

This paper provides a semidefinite programming approach to an identification of linear systems with roughly quantized outputs. Measurement data sampled from low resolution sensors have large quantization errors, which deteriorate the identification accuracy. The identification problem is formulated into nonlinear and nonconvex programming, however, the proposed approach provides a new method to obtain an approximate optimal value via recursive semidefinite programming. Numerical examples demonstrate that we can estimate both plant parameters and true output and show the effectiveness of the proposed method.