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This paper deals with the colorization-based image coding algorithm. In this algorithm, a color image is compressed by encoding its luminance image by a standard coding method such as JPEG coding and by storing several color pixels called as representative pixels (RPs). In decoding phase, a color image is restored from a luminance image and some color information of RPs using the image colorization technique. While previous studies have achieved a high coding performance, the compression method of RPs has not been considered because the positions of RPs are inhomogeneous. In order to improve the image coding performance, this paper proposes the RPs compression algorithm using the graph Fourier transform, where the chrominance image is transformed to graph spectrum and compressed. Using this RPs compression algorithm and a colorization technique, a new colorization-base image coding algorithm is proposed. Numerical results show that the proposed algorithm achieves better performance than some previous studies and JPEG2000 coding.

This paper deals with a problem of matrix completion in which each column vector of the matrix belongs to a low-dimensional differentiable manifold (LDDM), with the target matrix being high or full rank. To solve this problem, algorithms based on polynomial mapping and matrix-rank minimization (MRM) have been proposed; such methods assume that each column vector of the target matrix is generated as a vector in a low-dimensional linear subspace (LDLS) and mapped to a pth order polynomial and that the rank of a matrix whose column vectors are dth monomial features of target column vectors is deficient. However, a large number of columns and observed values are needed to strictly solve the MRM problem using this method when p is large; therefore, this paper proposes a new method for obtaining the solution by minimizing the rank of the submatrix without transforming the target matrix, so as to obtain high estimation accuracy even when the number of columns is small. This method is based on the assumption that an LDDM can be approximated locally as an LDLS to achieve high completion accuracy without transforming the target matrix. Numerical examples show that the proposed method has a higher accuracy than other low-rank approaches.

This paper deals with a problem of matrix completion in which each column vector of the matrix belongs to a low-dimensional differentiable manifold (LDDM), with the target matrix being high or full rank. To solve this problem, algorithms based on polynomial mapping and matrix-rank minimization (MRM) have been proposed; such methods assume that each column vector of the target matrix is generated as a vector in a low-dimensional linear subspace (LDLS) and mapped to a p-th order polynomial, and that the rank of a matrix whose column vectors are d-th monomial features of target column vectors is defficient. However, a large number of columns and observed values are needed to strictly solve the MRM problem using this method when p is large; therefore, this paper proposes a new method for obtaining the solution by minimizing the rank of the submatrix without transforming the target matrix, so as to obtain high estimation accuracy even when the number of columns is small. This method is based on the assumption that an LDDM can be approximated locally as an LDLS to achieve high completion accuracy without transforming the target matrix. Numerical examples show that the proposed method has a higher accuracy than other low-rank approaches.

This paper proposes a novel image steganography algorithm for color image. Recently, colorization-based image coding technique has been studied. In order to compress the color image effectively, this technique transform the chrominance image to a vector in a low-dimensional subspace via the colorization matrix. This paper utilizes the colorization-based image coding for steganography algorithm, where the secret data is embedded into the null space of the colorization matrix. Because the null space is high dimension enough, a large capacity data can be embedded. Numerical examples show that the proposed algorithm embeds large capacity secret data such as grayscale image into color image effectively.

This paper proposes a new algorithm for image inpainting algorithm based on the matrix rank minimization and locally linear embedding (LLE) method. Assuming that intensity values of an image belong to an unknown manifold, which can be mapped into a linear subspace by an unknown function, the image inpainting problem is formulated as minimizing sum of rank of submatrices of Hankel matrix. In order to solve the problem, this paper modifies the iterative partial matrix shrinkage (IPMS) algorithm and provides an inpainting algorithm. Numerical examples show that the proposed algorithm recovers missing pixels efficiently.

It has become critical to develop explanatory models using partial differential equations (PDEs) for big data from interesting scientific phenomena, e.g., fluids, atmosphere, and cosmic phenomena. Big data are often measured at discrete spatiotemporal points. In this paper, we assume a PDE and consider a set of the PDE solution data at multiple discrete points as pseudo-measurement data. In a data-driven PDE derivation, it is assumed that the PDE is a linear regression model comprising partial temporal and spatial differential terms, where the coefficients are estimated using regression analysis techniques, and the PDE derivation accuracy is defined as the difference (i.e., error) between the exact and estimated coefficients. A spatiotemporal model is required to calculate the partial temporal and spatial differential terms; thus, we employ a spatiotemporal model based on a neural network (NN) obtained from big data. To develop the data-driven PDE derivation technique, we employ PDEs with exact solutions such that we can calculate the differential terms by differentiating them analytically at multiple discrete points. If we assume an activation function in the NN model, the partial differential term can be derived using a chain rule. The NN model accuracy is measured by the loss function and error between the exact and estimated partial differential terms. In addition, we clarify a requirement for an NN structure that can maximize the PDE derivation and NN model accuracy by varying the NN meta-parameters, i.e., the numbers of NN layers and neurons.

Since amount of big data is extremely huge, low-delay and low-complexity signal processing devices are strongly required in big data signal processing. Digital filters are the key device for digital signal processing. Digital filters with sparse coefficients (0 coefficients) are beneficial to reduce the computational complexity. This paper proposes a design method for low-delay FIR filters with sparse coefficients. We consider the optimization of combination of selection for sparse coefficients. If the sparse coefficients are selected, the real coefficients can be computed based on the Lagrange multiplier method. We employ the branch and bound method incorporated with the Lagrange multiplier method. Also, we propose a selection method of the initial cost for high-speed search. The feature of this method is as follows: (a) The number of 0 coefficients can explicitly specify. (b) The optimality is guaranteed in the least squares sense. We present a design example in order to demonstrate the effectiveness of our method.

Excessive increase in blood glucose level after eating increases the risk of macroangiopathy, and a method for not increasing the postprandial blood glucose level is desired. However, a logical design method of the dietary ingestion pattern controlling the postprandial blood glucose level has not yet been established. We constructed a mathematical model of blood glucose control by oral glucose ingestion in three healthy human subjects, and predicted that intermittent ingestion 30 min apart was the optimal glucose ingestion patterns that minimized the peak value of blood glucose level. We confirmed with subjects that this intermittent pattern consistently decreased the peak value of blood glucose level. We also predicted insulin minimization pattern, and found that the intermittent ingestion 30 min apart was optimal, which is similar to that of glucose minimization pattern. Taken together, these results suggest that the glucose minimization is achieved by suppressing the peak value of insulin concentration, rather than by enhancing insulin concentration. This approach could be applied to design optimal dietary ingestion patterns., The key points of this study are three-fold: The first point is the physiological impact. Intuitively, an ingestion pattern that minimizes the maximum blood glucose level is expected to be a slow, continuous ingestion. We found that the optimal minimization pattern was an intermittent pattern with 30 min intervals. The second point is the methodology. We constructed the mathematical model as a forward problem, and in turn, predicted input pattern by control the output pattern of interest as an inverse problem. The third point is the experiment design used to generate the mathematical model; dense time course data for six ingestion patterns combining of 3 doses of glucose level and 2 durations of ingestion.

Atopic dermatitis (AD) is a chronic inflammatory skin disease, affecting up to 25% of children worldwide. While the current mainstay of AD treatment is topical application of corticosteroids and emollients, clear guidance for effective use of these treatments, such as the frequency, duration and potency, are not fully established. This paper proposes a computational method to design personalized treatment strategies for AD by applying model predictive control (MPC) to a hybrid nonlinear mathematical model of AD pathogenesis. We demonstrate that our method can suggest effective schedules for corticosteroid treatments that can achieve long-term management of moderate to severe AD symptoms. The proposed MPC uses a single linearized model of AD for prediction of disease progression based on daily measurement of the disease state, and provides a computational framework to suggest personalized treatment strategies with a small computational burden.

Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we used compressed sensing technology and developed a system identification method using data of different time scales by recovering signals of missing time points. We measured phosphorylation of ERK and CREB, immediate early gene expression products, and mRNAs of decoder genes for neurite elongation in PC12 cell differentiation and performed system identification, revealing the input–output relationships between signaling and gene expression with sensitivity such as graded or switch-like response and with time delay and gain, representing signal transfer efficiency. We predicted and validated the identified system using pharmacological perturbation. Thus, we provide a versatile method for system identification using data with different time scales., Author summary The key points of this study are two-fold: The first point is the decoding mechanism for cell differentiation. We previously demonstrated the encoding mechanism of cell fate decision information by transient and sustained ERK activation in PC12 cells, and also identified the decoding genes essential for cell differentiation in PC12 cells, including Metrnl, Dclk1, and Serpinb1a, denoted as LP (latent process) genes, which are the decoders of neurite length information. Importantly, the expression levels of the LP genes, but not the phosphorylation level of ERK, correlate with neurite length. Thus, the decoding mechanism of signaling activities by LP gene expression is a key issue for understanding the mechanism of cell differentiation. Here we identified a selective NGF- and PACAP-signaling decoding system by LP gene expression for neurite extension by developing a system identification method. The second point is the modeling. Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we developed a signal recovery technique in the field of compressed sensing originally developed for image analysis to biological sparse data of different time scales of signaling and gene expression.