25 accepted papers
We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting algorithm with two steps: (i) a time-varying forward step with…
The equilibrium selection problem in the generalized Nash equilibrium problem (GNEP) has recently been studied as an optimization problem, defined over the set of all variational equilibria achievable through a lower-level non-cooperative game among players. However, to make such a selection fair fo…
We propose a variable smoothing algorithm for solving nonconvexly constrained nonsmooth optimization problems. The target problem has two issues that need to be addressed: (i) the nonconvex constraint and (ii) the nonsmooth term. To handle the nonconvex constraint, we translate the target problem in…
The generalized minimax concave (GMC) penalty is a nonconvex sparse regularizer which can preserve the overall-convexity of the sparse least squares problem. In this paper, we study the solution path of a special but important instance of the GMC model termed the scaled GMC (sGMC) model. We show tha…
For the constrained LiGME model, a nonconvexly regularized least squares estimation model, under its overall convexity condition, we newly present an iterative algorithm of guaranteed convergence to its globally optimal solution. The proposed algorithm can deal with two different types of constraint…
In this paper, we propose a novel sparse adaptive filtering algorithm termed compensated shrinkage affine projection algorithm (CS-APA). Our cost function is the sum of a time-varying data fidelity term and a difference-of-convex (DC) type nonconvex sparse regularizer. The regularizer includes the w…
Optimization problem with orthogonality constraints, whose feasible region is called the Stiefel manifold, has rich applications in data sciences. The severe non-linearity of the Stiefel manifold has hindered the utilization of optimization mechanisms developed specially over a vector space for the…
In this paper, we propose a novel strategy which utilizes an inherent algebraic property of simultaneously diagonalizable matrix tuples, i.e., commutativity, for both (i) reducing approximate CP decomposition of a higher-order tensor to Approximate Simultaneous Diagonalization (ASD) and (ii) solving…
In this paper, we present a novel formulation of Approximate Simultaneous Diagonalization (ASD) with a nonconvex feasibility problem to find a structured low rank matrix whose building blocks are the Kronecker sums of given multiple matrices. To tackle this feasibility problem, we propose an alterna…
In this paper, we propose a new linearly involved convexity-preserving model for signal recovery by extending the idea in the generalized minimax concave (GMC) penalty [Se-lesnick' 17]. The proposed model can use nonconvex penalties but maintain the overall convexity and is applicable to much more g…
Expressing multidimensional information as a value in hypercomplex number systems (e.g., quaternion, octonion, etc.) has great potential, in data sciences, e.g., signal processing, to enjoy their nontrivial algebraic benefits which are not available in standard real or complex vector systems. Strate…
Identification of piecewise continuous Hammerstein systems, which consist of the cascade of memoryless piecewise continuous systems followed by linear systems, is an important problem in engineering. In the identification process, major existing approaches approximate exact minimization of the non-c…
We propose a novel automatic shrinkage tuning technique for the adaptive proximal forward-backward splitting (APFBS) algorithm. The shrinkage tuning aims to choose an appropriate value of the shrinkage parameter and achieve minimal system mismatch as possible. The system mismatch is approximated bas…
Expressing multidimensional information as a value in hypercomplex number systems (e.g., quaternion, octonion, etc.) has great potential, in signal processing applications, to enjoy their nontrivial algebraic benefits which are not available in standard real or complex vector systems. Strategic util…
The hybrid steepest descent method (HSDM) [Yamada, '01] was introduced as a low-computational complexity tool for solving convex variational-inequality problems over the fixed-point set of non-expansive mappings in Hilbert spaces. Motivated by results on decentralized optimization, this study introd…
In 2013, Nguyen and Yamada proposed Adaptive normalized quasi-Newton algorithm and its adaptive step size for accurate and stable extraction of the first generalized eigenvector. The adaptive step size is determined by an upper bound of the condition number of a time-varying matrix. However, the emp…
Exploiting the sparsity in learning algorithms is a key to achieve excellent performances of adaptive filters. This can be realized by the adaptive proximal forward-backward splitting with carefully chosen parameters. In this paper, we propose an automatic parameter tuning based on a minimization pr…
Finding a common point of multiple closed sets in a real Hilbert space has been an important task in a wide range of signal processing. In this paper, we study asymptotic properties of the parallel projection method (PPM) for closed sets satisfying a special feasibility condition, which holds in the…
This paper proposes fast iterative algorithms for solving convexly constrained spline smoothing through a characterization of solutions in a primal-dual space. In view of achievements for fast implementations of spline interpolation, the update of the proposed algorithm is designed as the compositio…
Nguyen and Yamada [NY'13] proposed an adaptive algorithm for fast and stable extraction of the first generalized Hermitian eigenvector and mentioned the extension to the first r generalized eigenvector extraction based on the nested orthogonal complement structure [NTY'12]. However, we recently foun…
Spline is a piecewise polynomial and has been widely used for interpolation and smoothing of observed data. In this paper, with the use of the sufficient condition, derived by Heß and Schmidt, for the nonnegativity of bivariate splines on square grid, we propose two-dimensional positive spline inter…
Two-dimensional (2D) phase unwrapping is a reconstruction problem of a continuous phase, defined over 2D-domain, from its wrapped samples. In our previous work, we presented a two-step phase unwrapping algorithm which first constructs, as the real and imaginary parts of a complex function, a pair of…
Spline is a continuous function piecewise-defined by polynomials and is widely used for interpolation and smoothing of observed data. In 1994, Heβ and Schmidt proposed a positive quartic C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -spline…
In this paper, we propose a new modeling technique of signals having time-varying spectral patterns for supervised source separation. Typical examples of such signals are instrumental sounds having several segments such as “attack” and “sustain”. In the proposed technique, a given signal is modeled…
This paper proposes a second-order discrete total generalized variation (TGV) for arbitrary graph signals, which we call the graph TGV (G-TGV). The original TGV was introduced as a natural higher-order extension of the well-known total variation (TV) and is an effective prior for piecewise smooth si…