arXiv subjects

Daichi Kitahara

Publications and source records attributed to Daichi Kitahara.

5 recordsLinked to original sources

arXiv2026

One-Dimensional Nonnegative Spline Smoothing via Convex Semi-Infinite Programming with a Cutting-Plane Method

Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of spline functions because necessary and sufficient conditions for the nonnegativity are infinitely many linear inequalities, which are difficult to handle in optimization algorithms. This conventional method quickly computes a nonnegative spline function via quadratic programming (QP), but the optimal solution may be slightly degraded by using the sufficient condition. In this paper, we express 1D nonnegative spline smoothing as a convex semi-infinite programming (CSIP) problem that directly deals with infinite inequality constraints. As optimization algorithms for general SIP problems, local-reduction-based sequential quadratic programming (LRSQP) methods are used, but their convergence performance deteriorates for certain problems due to multiple approximations during updates. To quickly solve the CSIP problem, we propose a cutting-plane (CP) method. In the proposed method, after giving an initial solution by the standard spline smoothing, we find the minimizer of each polynomial piece by using the closed-form solution for a low-degree polynomial or a numerical solution for a high-degree polynomial. If the minimum value is negative, then such minimizer is added into the constraint of the problem to guarantee the nonnegativity. This constrained problem is quickly solved via QP, and we find the minimizer of each polynomial piece again. We repeat these procedures until there are no negative minimum values. The proposed method guarantees convergence to the original CSIP solution, and its effectiveness is demonstrated in numerical experiments by comparison to the conventional methods, QP under the sufficient condition and CSIP using the MATLAB LRSQP algorithm.

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arXiv2023

Convex Estimation of Sparse-Smooth Power Spectral Densities from Mixtures of Realizations with Application to Weather Radar

In this paper, we propose a convex optimization-based estimation of sparse and smooth power spectral densities (PSDs) of complex-valued random processes from mixtures of realizations. While the PSDs are related to the magnitude of the frequency components of the realizations, it has been a major challenge to exploit the smoothness of the PSDs, because penalizing the difference of the magnitude of the frequency components results in a nonconvex optimization problem that is difficult to solve. To address this challenge, we design the proposed model that jointly estimates the complex-valued frequency components and the nonnegative PSDs, which are respectively regularized to be sparse and sparse-smooth. By penalizing the difference of the nonnegative variable that estimates the PSDs, the proposed model can enhance the smoothness of the PSDs via convex optimization. Numerical experiments on the phased array weather radar, an advanced weather radar system, demonstrate that the proposed model achieves superior estimation accuracy compared to existing sparse estimation models, regardless of whether they are combined with a smoothing technique as a post-processing step or not.

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arXiv2021

Design of Tight Minimum-Sidelobe Windows by Riemannian Newton's Method

The short-time Fourier transform (STFT), or the discrete Gabor transform (DGT), has been extensively used in signal analysis and processing. Their properties are characterized by a window function. For signal processing, designing a special window called tight window is important because it is known to make DGT-domain processing robust to error. In this paper, we propose a method of designing tight windows that minimize the sidelobe energy. It is formulated as a constrained spectral concentration problem, and a Newton's method on an oblique manifold is derived to efficiently obtain a solution. Our numerical example showed that the proposed algorithm requires only several iterations to reach a stationary point.

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arXiv2020

Frequency-Undersampled Short-Time Fourier Transform

The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix becomes more than twice the signal length, and hence STFT is hardly used for signal compression. In addition, even if we modify the spectrogram into a desired one by spectrogram-based signal processing, it is re-changed during the inversion as long as it is outside the range of STFT. In this paper, to reduce the number of components of a spectrogram while maintaining the analytical ability, we propose the frequency-undersampled STFT (FUSTFT), which computes only half the frequency components. We also present the inversions with and without the periodic condition, including their different properties. In simple numerical examples of audio signals, we confirm the validity of FUSTFT and the inversions.

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arXiv2019

Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they consist of simple operations, handling the terms in the objective function separately. In this overview, we demystify a selection of recent proximal splitting algorithms: we present them within a unified framework, which consists in applying splitting methods for monotone inclusions in primal-dual product spaces, with well-chosen metrics. Along the way, we easily derive new variants of the algorithms and revisit existing convergence results, extending the parameter ranges in several cases. In particular, we emphasize that when the smooth term in the objective function is quadratic, e.g., for least-squares problems, convergence is guaranteed with larger values of the relaxation parameter than previously known. Such larger values are usually beneficial for the convergence speed in practice.

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