In this paper, we propose a depth-aided color image inpainting method in the quaternion domain, called depth-aided low-rank quaternion matrix completion (D-LRQMC). In conventional quaternion-based inpainting techniques, the color image is expressed as a quaternion matrix by using the three imaginary parts as the color channels, whereas the real part is set to zero and has no information. Our approach incorporates depth information as the real part of the quaternion representations, leveraging the correlation between color and depth to improve the result of inpainting. In the proposed method, we first restore the observed image with the conventional LRQMC and estimate the depth of the restored result. We then incorporate the estimated depth into the real part of the observed image and perform LRQMC again. Simulation results demonstrate that the proposed D-LRQMC can improve restoration accuracy and visual quality for various images compared to the conventional LRQMC. These results suggest the effectiveness of the depth information for color image processing in quaternion domain.

We propose a complex-domain pitch estimation algorithm for narrowband speech signals, which utilizes a complex spectrum containing both amplitude and phase spectrum information. Traditional frequency-domain pitch estimation algorithms assume that a speech signal has a harmonic structure; they estimate a pitch by calculating the distance between the adjacent peaks of the amplitude spectrum corresponding to harmonics. However, only a few peaks can be detected from narrowband speech signals because of their limited bandwidth, resulting in pitch estimation errors. In this article, phase differences between harmonics are utilized as an additional cue for pitch estimation. The phase difference between harmonics refers to the two-step phase difference between successive analysis frames and between the lowest-order harmonic and other harmonics, which is theoretically derived using the pitch. When the phase spectrum for the higher-order harmonic is shifted by the theoretical value, it agrees with the phase spectrum for the lowest-order harmonic. Therefore, for each pitch candidate, the proposed method calculates the shifted phase spectra and combines them with the amplitude spectrum to generate complex spectra. When a pitch candidate is correct, the cumulative sum of the complex spectra is added in the same direction, which emphasizes harmonics even for narrowband speech signals. Results of the objective evaluation show that the proposed method accurately estimates the pitch from narrowband speech signals.

This paper proposes a noise reduction method for reducing impact noise. The proposed method is based on a zero phase (ZP) signal which is defined as the IDFT of a spectral amplitude. The ZP signal of the impact noise has zero values except of around the origin, since its spectral amplitude is almost flat. When a speech signal has periodicity, its ZP signal has also periodicity. Hence, when the speech signal mixed with the impact noise, the noise can be reduced by replacing samples around the origin with samples around the second period of the ZP signal. A practical impact noise often has damped oscillation which is similar to a periodic signal. Under the assumption that the pitch of the damped oscillation is higher than one of speech, we detect and reduce the damped oscillation by introducing an additional pitch estimator into the ZP replacement method.

This paper presents a learning method of a structuring element for morphological image generative model by using a maximum a posterior (MAP) estimation. Mathematical morphology provides set-theoretic image processing methods. In the morphological processing, an image is approximated as a union of translated and level-shifted structuring elements. The specification of the structuring element is crucial to application of the morphology for image processing tasks. In this paper, we introduce the MAP estimation of the structuring element from an input image for the morphological modeling. Sparse prior density functions of approximation errors and occurrence of the structuring elements are assumed for the learning. The structuring element is optimized to maximize the likelihood that is estimated from the prior density functions. In experiments, we show that the proposed learning method is capable to extract fundamental micro-structures of texture images as the structuring elements.

In this paper, we introduce shift-invariant sparse image representations using tree-structured dictionaries. Sparse coding is a generative signal model that approximates signals by the linear combinations of atoms in a dictionary. Since a sparsity penalty is introduced during signal approximation and dictionary learning, the dictionary represents the primal structures of the signals. Under the shift-invariance constraint, the dictionary comprises translated structuring elements (SEs). The computational cost and number of atoms in the dictionary increase along with the increasing number of SEs. In this paper, we propose an algorithm for shift-invariant sparse image representation, in which SEs are learnt with a tree-structured approach. By using a tree-structured dictionary, we can reduce the computational cost of the image decomposition to the logarithmic order of the number of SEs. We also present the results of our experiments on SE learning and the use of our algorithm in an image recovery application.

The high resolution image restoration method from a down-sampled low resolution image by using the discrete cosine transform (DCT) is proposed. The downsampling process is modeled in matrix form and the similar transformation by the DCT matrix makes the downsampling matrix to be a sparse matrix. Then the restored high resolution image can be expressed in a scalar form by using the similar transformation and efficiently computed from the low resolution image. Computer simulations show that the proposed method is superior to the cubic spline interpolation in the high resolution image restoration performance.

An online recognition method for handwritten Hiragana characters is developed based upon a complex AR model. The time delay of the AR model is enlarged so that global attributes of handwritten characters are well incorporated into the model, and a character segmentation technique is developed for performance improvement. A good recognition score has been obtained for two different writers.

This paper investigates the application of a radial basis function network (RBFN) to a hierarchical image coding for progressive transmission. The RBFN is then used to generate an interpolated image from the subsampled version. An efficient method of computing the network parameters is developed for reduction in computational and memory requirements. The coding method does not suffer from problems of blocking effect and can produce the coarsest image quickly. Quantization error effects introduced at one stage are considered in decoding images at the following stages, thus allowing lossless progressive transmission.

A hierarchical coding system for progressive image transmission that uses the generalization and learning capability of CMAC (cerebellar model arithmetic computer or cerebellar model articulation controller) is described. Each encoder and decoder includes a set of CMACs having different widths of generalization region. A CMAC with a wider generalization region is used to learn a lower frequency component of the original image. The training signals for each CMAC are progressively transmitted to a decoder. Compression is achieved by decreasing the number of training signals for CMAC with a wider generalization region, and by making quantization intervals wider for CMAC with a smaller generalization region. CMACs in the decoder are trained on the training signals to be transmitted. The output is recursively added to the other so that the quality of image reconstruction is gradually improved. The proposed method, unlike the conventional hierarchical coding methods, uses no filtering technique in both decimation and interpolation processes, and has the following advantages: (i) it does not suffer from problems of blocking effect; (ii) the computation includes no multiplication; (iii) the coarsest reconstructed image is quickly produced; (iv) the total number of transmitted data is equal to the number of the original image pixels; (v) all the reconstructed images are equal to the original image in size; (vi) quantization errors introduced at one level can be taken into account at the next level, allowing lossless progressive image transmission.

The authors present a novel nonlinear regulator design method that integrates linear optimal control techniques and nonlinear neural network learning methods. Multilayered neural networks are used to add nonlinear effects to the linear optimal regulator (LOR). The regulator can compensate for nonlinear system uncertainties that are not considered in the LOR design and can tolerate a wider range of uncertainties than the LOR alone. The salient feature of the regulator is that the control performance is much improved by using a priori knowledge of the plant dynamics as the system equation and the corresponding LOR. Computer simulations are performed to show the applicability and the limitations of the regulator.

The authors present a nonlinear regulator design method that uses multilayered neural networks (MNNs) for nonlinear systems operating in the presence of system uncertainties. The regulator consists of two MNNs for modeling and control in addition to the classical linear optimal regulator. The MNN for modeling is connected in parallel with the system equation to compensate for system uncertainties. The MNN for control is connected in parallel with the linear optimal regulator to compensate for the control errors caused by system uncertainties. Both MNNs are trained so that a desired response of the plant is obtained. A training signal of the MNN for control is acquired through the results of modeling. It is shown that the regulator can generate more sophisticated control inputs than the linear optimal regulator, even when the MNNs get stuck at local minima. A priori knowledge of the plant dynamics can be incorporated into the system equation and into the corresponding linear optimal regulator. The learning time is greatly reduced as compared with the case where MNN is used alone for modeling or control. Numerical simulations show that the regulator can stabilize a plant that is not stabilized by the linear regulator

In this paper, first, the normalized Triangular Lattice and Escalator algorithms for recursive least squares estimation are presented. Next, roundoff errors of both algorithms in fixed point arithmetic are analyzed and compared. Expressions are derived for the biases in the estimated coefficients due to roundoff errors. By improving the method of analysis, better expressions are obtained, as compared with the previous ones.