• Journal of the Korean Mathematical Society
• /
• v.44 no.6
• /
• pp.1281-1290
• /
• 2007

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

• Journal of Information Processing Systems
• /
• v.13 no.5
• /
• pp.1168-1182
• /
• 2017

In the past decades, various image regularization methods have been introduced. Among them, total variation model has drawn much attention for the reason of its low computational complexity and well-understood mathematical behavior. However, regularization parameter estimation of total variation model is still an open problem. To deal with this problem, a novel adaptive regularization parameter selection scheme is proposed in this paper, by means of using the local spectral response, which has the capability of locally selecting the regularization parameters in a content-aware way and therefore adaptively adjusting the weights between the two terms of the total variation model. Experiment results on simulated and real noisy image show the good performance of our proposed method, in visual improvement and peak signal to noise ratio value.

• Current Optics and Photonics
• /
• v.5 no.3
• /
• pp.322-328
• /
• 2021

In this paper, a pretreatment method for a matrix in convex optimization is proposed to optimize the spectral reconstruction process of a disordered dispersion spectrometer. Unlike the reconstruction process of traditional spectrometers using Fourier transforms, the reconstruction process of disordered dispersion spectrometers involves solving a large-scale matrix equation. However, since the matrices in the matrix equation are obtained through measurement, they contain uncertainties due to out of band signals, background noise, rounding errors, temperature variations and so on. It is difficult to solve such a matrix equation by using ordinary nonstationary iterative methods, owing to instability problems. Although the smoothing Tikhonov regularization approach has the ability to approximatively solve the matrix equation and reconstruct most simple spectral shapes, it still suffers the limitations of reconstructing complex and irregular spectral shapes that are commonly used to distinguish different elements of detected targets with mixed substances by characteristic spectral peaks. Therefore, we propose a special pretreatment method for a matrix in convex optimization, which has been proved to be useful for reducing the condition number of matrices in the equation. In comparison with the reconstructed spectra gotten by the previous ordinary iterative method, the spectra obtained by the pretreatment method show obvious accuracy.

• Journal of the Optical Society of Korea
• /
• v.20 no.6
• /
• pp.752-761
• /
• 2016

Hyperspectral images are often contaminated with stripe noise, which severely degrades the imaging quality and the precision of the subsequent processing. In this paper, a variational model is proposed by employing spectral-spatial adaptive unidirectional variation and a sparse representation. Unlike traditional methods, we exploit the spectral correction and remove stripes in different bands and different regions adaptively, instead of selecting parameters band by band. The regularization strength adapts to the spectrally varying stripe intensities and the spatially varying texture information. Spectral correlation is exploited via dictionary learning in the sparse representation framework to prevent spectral distortion. Moreover, the minimization problem, which contains two unsmooth and inseparable $l_1$-norm terms, is optimized by the split Bregman approach. Experimental results, on datasets from several imaging systems, demonstrate that the proposed method can remove stripe noise effectively and adaptively, as well as preserve original detail information.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.29 no.12 s.243
• /
• pp.1597-1604
• /
• 2005

The identification of a moving noise source is important in reducing the source power of the transport systems such as airplanes or high speed trains. However, the direct measurement using a microphone running with noise source is usually difficult due to wind noise, white the source motion distorts the frequency characteristics of the pass-by sound measured at a fixed point. In this study the relationship between the spectra of the source and the pass-by sound signal is analyzed for an acoustic source moving at a constant velocity. Spectrum of the sound signal measured at a fixed point has an integral relationship with the source spectrum. Nevertheless direct conversion of the measured spectrum to the source spectrum is ill-posed due to the singularity of the integral kernel. Alternatively a differential equation approach is proposed, where the source characteristics can be recovered by solving a differential equation relating the source signal to the distorted measurement in time domain. The parameters such as the source speed and the time origin, required beforehand, are also determined only from the frequency-phase relationship using an auxiliary measurement. With the help of the regularization method, the source signal is successfully recovered. The effects of the parameter errors to the estimated frequency characteristics of the source are investigated through numerical simulations.

• KIPS Transactions on Computer and Communication Systems
• /
• v.9 no.11
• /
• pp.265-272
• /
• 2020

In the research of brain computer interface (BCI) technology, one of the big problems encountered is how to deal with some people as called the BCI-illiteracy group who could not control the BCI system. To approach this problem efficiently, we investigated a kind of spectral EEG characteristics in the prior resting state in association with BCI performance in the following BCI tasks. First, spectral powers of EEG signals in the resting state with both eyes-open and eyes-closed conditions were respectively extracted. Second, a convolution neural network (CNN) based binary classifier discriminated the binary motor imagery intention in the BCI task. Both the linear correlation and binary prediction methods confirmed that the spectral EEG characteristics in the prior resting state were highly related to the BCI performance in the following BCI task. Linear regression analysis demonstrated that the relative ratio of the 13 Hz below and above the spectral power in the resting state with only eyes-open, not eyes-closed condition, were significantly correlated with the quantified metrics of the BCI performance (r=0.544). A binary classifier based on the linear regression with L1 regularization method was able to discriminate the high-performance group and low-performance group in the following BCI task by using the spectral-based EEG features in the precedent resting state (AUC=0.817). These results strongly support that the spectral EEG characteristics in the frontal regions during the resting state with eyes-open condition should be used as a good predictor of the following BCI task performance.

• Journal of the Society of Naval Architects of Korea
• /
• v.52 no.1
• /
• pp.88-95
• /
• 2015

For the frequency-domain spectral fatigue analysis, the probability density function of stress range needs to be estimated based on the stress spectrum only, which is a frequency domain representation of the response. The probability distribution of the stress range of the narrow-band spectrum is known to follow the Rayleigh distribution, however the PDF of wide-band spectrum is difficult to define with clarity due to the complicated fluctuation pattern of spectrum. In this paper, efforts have been made to figure out the links between the probability density function of stress range to the structural response of wide-band Gaussian random process. An artificial neural network scheme, known as one of the most powerful system identification methods, was used to identify the multivariate functional relationship between the idealized wide-band spectrums and resulting probability density functions. To achieve this, the spectrums were idealized as a superposition of two triangles with arbitrary location, height and width, targeting to comprise wide-band spectrum, and the probability density functions were represented by the linear combination of equally spaced Gaussian basis functions. To train the network under supervision, varieties of different wide-band spectrums were assumed and the converged probability density function of the stress range was derived using the rainflow counting method and all these data sets were fed into the three layer perceptron model. This nonlinear least square problem was solved using Levenberg-Marquardt algorithm with regularization term included. It was proven that the network trained using the given data set could reproduce the probability density function of arbitrary wide-band spectrum of two triangles with great success.