This letter presents a simple and explicit formulation of non-unique Wiener filters associated with the linear predictor for processing of sinusoids. It was shown in the literature that, if the input signal consists of only sinusoids and does not include a white noise, the input autocorrelation matrix in the Wiener-Hopf equation becomes rank-deficient and thus the Wiener filter is not uniquely determined. In this letter we deal with this rank-deficient problem and present a mathematical description of non-unique Wiener filters in a simple and explicit form. This description is directly obtained from the tap number, the frequency of sinusoid, and the delay parameter. We derive this result by means of the elementary row operations on the augmented matrix given by the Wiener-Hopf equation. We also show that the conventional Wiener filter for noisy input signal is included as a special case of our description.

This paper proposes statistical analysis of phase-only correlation functions based on linear statistics and directional statistics. We derive the expectation and variance of the phase-only correlation functions assuming phase-spectrum differences of two input signals to be probability variables. We first assume linear probability distributions for the phase-spectrum differences. We next assume circular probability distributions for the phase-spectrum differences, considering phase-spectrum differences to be circular data. As a result, we can simply express the expectation and variance of phase-only correlation functions as linear and quadratic functions of circular variance of phase-spectrum differences, respectively.

In this paper, we propose to employ an extension to the natural gradient algorithm for robust Independent Component Analysis against outliers. The standard natural gradient algorithm does not exhibit this property since it employs nonrobust sample estimates for computing higher order moments. In order to overcome this drawback, we propose to use robust alternatives to higher order moments, which are comparatively less sensitive to outliers in the observed data. Some computer simulations are presented to show that the proposed method, as compared to the standard natural gradient algorithm, gives better performance in the presence of outlying data.

This letter proposes performance evaluation of phase-only correlation (POC) functions using signal-to-noise ratio (SNR) and peak-to-correlation energy (PCE). We derive the general expressions of SNR and PCE of the POC functions as correlation performance measures. SNR is expressed by simple fractional function of circular variance. PCE is simply given by squared peak value of the POC functions, and its expectation can be expressed in terms of circular variance.

In the field of adaptive notch filtering, Monotonically Increasing Gradient (MIG) algorithm has recently been proposed by Sugiura and Shimamura [1], where it is claimed that the MIG algorithm shows monotonically increasing gradient characteristics. However, our analysis has found that the underlying theory in [1] includes crucial errors. This letter shows that the formulation of the gradient characteristics in [1] is incorrect, and reveals that the MIG algorithm fails to realize monotonically increasing gradient characteristics when the input signal includes white noise.

In this paper, we use a modified Gaussian filter to improve enlargement accuracy of the arbitrary scale LP enlargement method, which is based on the Laplacian pyramid representation (so called "LP method"). The parameters of the proposed algorithm are extracted through a theoretical analysis and an experimental estimation. Experimental results show that the proposed modified Gaussian filter is effective for the arbitrary scale LP enlargement method.

This paper proposes statistical analysis of phase-only correlation functions with phase-spectrum differences following wrapped distributions. We first assume phase-spectrum differences between two signals to be random variables following a linear distribution. Next, based on directional statistics, we convert the linear distribution into a wrapped distribution by wrapping the linear distribution around the circumference of the unit circle. Finally, we derive general expressions of the expectation and variance of the POC functions with phase-spectrum differences following wrapped distributions. We obtain exactly the same expressions between a linear distribution and its corresponding wrapped distribution.

In this paper, we propose an enlargement method for images with Gaussian noise based on the Laplacian pyramid (LP) representation. Unlike lowpass pre-processing approaches to the LP enlargement method, an embedded approach is used in this paper. Since the amplitude of Gaussian noise signals is smaller than the amplitude of image edge signals in the predicted LP stage, we adopt a modified ε-filter in the proposed LP enlargement algorithm to reduce the Gaussian noise. Experimental results show that the proposed method can obtain high accuracy denoise enlarged images.

The aim of this study is to improve the accuracy of flicker parameters estimation in old film sequences in which moving objects are present. Conventional methods tend to fail in flicker parameters estimation due to the effects of moving objects. Our proposed method firstly utilizes an adaptive Gaussian mixture model (GMM)-based method to detect the moving objects in the film sequences, and combines the detected results with the histogram-matched frames to generate reference frames for flicker parameters estimation. Then, on the basis of a linear flicker model, the proposed method uses an M-estimator with the reference frames to estimate the flicker parameters. Experimental results show that the proposed method can effectively improve the accuracy of flicker parameters estimation when the moving objects are present in the film sequences.

In this paper, we propose a novel bicubic method for digital image interpolation. Since the conventional bicubic method does not consider image local features, the interpolated images obtained by the conventional bicubic method often have a blurring problem. In this paper, the proposed bicubic method adopts both the local asymmetry features and the local gradient features of an image in the interpolation processing. Experimental results show that the proposed method can obtain high accuracy interpolated images.

A low-power SuperHTM embedded processor core, the SH-X2, has been designed in 90-nm CMOS technology. The power consumption was reduced by using hierarchical fine-grained clock gating to reduce the power consumption of the flip-flops and the clock-tree, synthesis and a layout that supports the implementation of the clock gating, and several-level power evaluations for RTL refinement. With this clock gating and RTL refinement, the power consumption of the clock-tree and flip-flops was reduced by 35% and 59%, including the process shrinking effects, respectively. As a result, the SH-X2 achieved 6,000 MIPS/W using a Renesas low-power process with a lowered voltage. Its performance-power efficiency was 25% better than that of a 130-nm-process SH-X.

A High performance digital filter LSI has been developed, which is suitable for two- or three-dimensional TV video signal processing. This 9th-order symmetrical transversal filter features high speed operation of 33 MHz. Moreover, the order and the transfer function of the filter are alterable. The chip, achieved through 2 µm CMOS technology, occupies about 50 mm2 and consumes less than 600 mW of power at a clock frequency of 33 MHz.

This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.

This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.

A new configuration is proposed for adaptive Rank Order Filters ('AROF') which adaptively extract the 'optimal rank'. The optimal rank is determined using the 'noise elimination efficiency' of ROF. The simulated results show that the AROF is more effective than the conventional rank-fixed ROFs at eliminating impulse noise.

This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.

To investigate the feasibility of a compact FEA image sensor with a large number of pixels, a 128 96 pixel FEA image sensor with a 4-µm-thick HARP target was fabricated and tested for the first time. The experimental results showed that the prototype could stably operate as a highly sensitive image sensor having both sufficient resolution corresponding to the number of pixels and a wide dynamic range, which demonstrated its potential as a next-generation image sensor.

This paper presents FIR digital filters based on stochastic/binary hybrid computation with reduced hardware complexity and high computational accuracy. Recently, some attempts have been made to apply stochastic computation to realization of digital filters. Such realization methods lead to significant reduction of hardware complexity over the conventional filter realizations based on binary computation. However, the stochastic digital filters suffer from lower computational accuracy than the digital filters based on binary computation because of the random error fluctuations that are generated in stochastic bit streams, stochastic multipliers, and stochastic adders. This becomes a serious problem in the case of FIR filter realizations compared with the IIR counterparts because FIR filters usually require larger number of multiplications and additions than IIR filters. To improve the computational accuracy, this paper presents a stochastic/binary hybrid realization, where multipliers are realized using stochastic computation but adders are realized using binary computation. In addition, a coefficient-scaling technique is proposed to further improve the computational accuracy of stochastic FIR filters. Furthermore, the transposed structure is applied to the FIR filter realization, leading to reduction of hardware complexity. Evaluation results demonstrate that our method achieves at most 40dB improvement in minimum stopband attenuation compared with the conventional pure stochastic design.

This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.

This paper derives the balanced realizations of second-order analog filters directly from the transfer function. Second-order analog filters are categorized into the following three cases: complex conjugate poles, distinct real poles, and multiple real poles. For each case, simple formulas are derived for the synthesis of the balanced realizations of second-order analog filters. As a result, we obtain closed form expressions of the balanced realizations of second-order analog filters.