In this paper, we have proposed a higher order non-linear PDE model containing diffusion terms of TV−L2 and TV−H−1 model for effective image denoising. Fourier spectral method for space and convexity ...splitting method for time have been used to solve the proposed PDE model. Stability analysis for the time discretized equation has been derived. Numerical experiment has been done on some test images and the results have been compared with the results of some existing models.
This paper deals with the joint design of Multiple-Input Multiple-Output (MIMO) radar transmit waveform and receive filter to enhance multiple targets detectability in the presence of ...signal-dependent (clutter) and independent disturbance. The worst-case Signal-to-Interference-Noise-Ratio (SINR) over multiple targets is explicitly maximized. To ensure hardware compatibility and the coexistence between MIMO radar and other wireless systems, constant modulus and spectral restrictions on the waveform are incorporated in our design. A max-min non-convex optimization problem emerges as a function of the transmit waveform, which we solve via a novel polynomial-time iterative procedure that involves solving a sequence of convex problems with constraints that evolve with every iteration. The overall algorithm follows an alternate optimization over the receive filter and transmit waveform. For the problem of waveform optimization (which is our central contribution), we provide analytical guarantees of monotonic cost function improvement with proof of convergence to a solution that satisfies the KarushKuhnTucker (KKT) conditions. We also develop extensions that address the well-known waveform similarity constraint. By simulating challenging practical scenarios, we evaluate the proposed algorithm against the state-of-the-art methods in terms of the achieved SINR value and the computational complexity. Overall, we show that our proposal outperforms state of the art competing methods while providing the most favorable performance-complexity balance.
Wireless powered communication (WPC) has been considered as one of the key technologies in the Internet of Things (IoT) applications. In this paper, we study a wireless powered time-division duplex ...(TDD) multiuser multiple-input multiple-output (MU-MIMO) system, where the base station (BS) has its own power supply and all users can harvest radio frequency (RF) energy from the BS. We aim to maximize the users' information rates by jointly optimizing the duration of users' time slots and the signal covariance matrices of the BS and users. Different to the commonly used sum rate and max-min rate criteria, the proportional fairness of users' rates is considered in the objective function. We first study the ideal case with the perfect channel state information (CSI), and show that the non-convex proportionally fair rate optimization problem can be transformed into an equivalent convex optimization problem. Then we consider practical systems with imperfect CSI, where the CSI mismatch follows a Gaussian distribution. A chance-constrained robust system design is proposed for this scenario, where the Bernstein inequality is applied to convert the chance constraints into the convex constraints. Finally, we consider a more general case where only partial knowledge of the CSI mismatch is available. In this case, the conditional value-at-risk (CVaR) method is applied to solve the distributionally robust system rate optimization problem. Simulation results are presented to show the effectiveness of the proposed algorithms.
In this paper we give a natural method of constructing a bi-stratified 0, 1-convexity by a 0, 1-valued interval operator, where the concept of bi-stratified 0, 1-convexities is firstly introduced. ...And its convex hull operators can be characterized by 0, 1-valued interval operators. Finally, we discuss the relationship between bi-stratified 0, 1-convexities and 0, 1-valued interval operators from a categorical aspect.
By our definition, “restricted Dirichlet-to-Neumann (DN) map” means that the Dirichlet and Neumann boundary data for a coefficient inverse problem (CIP) are generated by a point source running along ...an interval of a straight line.
On the other hand, the conventional DN data can be generated, at least sometimes, by a point source running along a hypersurface.
CIPs with restricted DN data are non-overdetermined in the
-dimensional case, with
.
We develop, in a unified way, a general and radically new numerical concept for CIPs with restricted DN data for a broad class of PDEs of second order, such as, e.g., elliptic, parabolic and hyperbolic ones.
Namely, using Carleman weight functions, we construct globally convergent numerical methods.
Hölder stability and uniqueness are also proved.
The price we pay for these features is a well-acceptable one in the numerical analysis, that is, we truncate a certain Fourier-like series with respect to some functions depending only on the position of the point source.
At least three applications are imaging of land mines, crosswell imaging and electrical impedance tomography.
A
bstract
Recently it was proposed that the theory space of effective field theories with consistent UV completions can be described as a positive geometry, termed the EFThedron. In this paper we ...demonstrate that at the core, the geometry is given by the convex hull of the product of two moment curves. This makes contact with the well studied bi-variate moment problem, which in various instances has known solutions, generalizing the Hankel matrices of couplings into moment matrices. We extend these solutions to hold for more general bi-variate problem, and are thus able to obtain analytic expressions for bounds, which closely match (and in some cases exactly match) numerical results from semi-definite programing methods. Furthermore, we demonstrate that crossing symmetry in the IR imposes non-trivial constraints on the UV spectrum. In particular, permutation invariance for identical scalar scattering requires that any UV completion beyond the scalar sector must contain arbitrarily high spins, including at least all even spins
ℓ
≤ 28, with the ratio of spinning spectral functions bounded from above, exhibiting large spin suppression. The spinning spectrum must also include at least one state satisfying a bound
m
J
2
<
M
h
2
J
2
−
12
J
4
−
32
J
2
+
204
8
150
−
43
J
2
+
2
J
4
, where
J
2
=
ℓ
(
ℓ
+1), and
M
h
is the mass of the heaviest spin 2 state in the spectrum.
In this paper, a novel non-orthogonal multiple access (NOMA) enhanced device-to-device (D2D) communication scheme is considered. Our objective is to maximize the system sum rate by optimizing ...subchannel and power allocation. We propose a novel solution that jointly assigns subchannels to D2D groups and allocates power to receivers in each D2D group. For the subchannel assignment, a novel algorithm based on the many-to-one two-sided matching theory is proposed for obtaining a suboptimal solution. Since the power allocation problem is nonconvex, sequential convex programming is adopted to transform the original power allocation problem to a convex one. The power allocation vector is obtained by iteratively tightening the lower bound of the original power allocation problem until convergence. Numerical results illustrate that: 1) the proposed joint subchannel and power allocation algorithm are an effective approach for obtaining near-optimal performance with acceptable complexity and 2) the NOMA enhanced D2D communication scheme is capable of achieving promising gains in terms of network sum rate and the number of accessed users, compared to a traditional OMA-based D2D communication scheme.
Standard stochastic optimization methods are brittle, sensitive to stepsize choice and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To ...address these challenges, we investigate models for stochastic optimization and learning problems that exhibit better robustness to problem families and algorithmic parameters. With appropriately accurate models—which we call the APROX family—stochastic methods can be made stable, provably convergent, and asymptotically optimal; even modeling that the objective is nonnegative is sufficient for this stability. We extend these results beyond convexity to weakly convex objectives, which include compositions of convex losses with smooth functions common in modern machine learning. We highlight the importance of robustness and accurate modeling with experimental evaluation of convergence time and algorithm sensitivity.
In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of
and
, we establish some quantum Ostrowski inequalities for twice quantum ...differentiable mappings involving
and
-quantum integrals. The results presented here are the generalization of already published ones.
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