Total Variation Norm Minimization Research Articles

Ray Tracing Acceleration Using Total Variation Norm Minimization for Radio Map Simulation

In this letter, a ray tracing (RT) acceleration method based on the total variation norm minimization (TVNM) scheme is presented. RT is a general tool used to analyze wireless communication environments. However, the simulation is time consuming because of the large number of ray calculations. This letter focuses on radio map interpolation as an acceleration approach. For radio map interpolation, we adopt TVNM, which is a representative edge-preserving interpolation method in the field of image processing. We regard the non-line-of-sight and line-of-sight region boundary as the edge of the radio map and use TVNM to achieve accurate interpolation. Furthermore, we consider known position selection to enhance the interpolation accuracy of TVNM. A computational simulation using commercial RT software revealed that the interpolation accuracy of the proposed method was better than those of other radio map interpolation methods and that RT simulation can be accelerated with an acceptable interpolation error.

Exact Recovery of Dirac Ensembles from the Projection Onto Spaces of Spherical Harmonics

In this work, we consider the problem of recovering an ensemble of Diracs on the sphere from its projection onto spaces of spherical harmonics. We show that under an appropriate separation condition on the unknown locations of the Diracs, the ensemble can be recovered through total variation norm minimization. The proof of the uniqueness of the solution uses the method of ‘dual’ interpolating polynomials and is based on Candès and Fernandez-Granda (Commun Pure Appl Math 67:906–956, 2014), where the theory was developed for trigonometric polynomials. We also show that in the special case of nonnegative ensembles, a sparsity condition is sufficient for exact recovery.

Exact recovery of non-uniform splines from the projection onto spaces of algebraic polynomials

In this work we consider the problem of recovering non-uniform splines from their projection onto spaces of algebraic polynomials. We show that under a certain Chebyshev-type separation condition on its knots, a spline whose inner-products with a polynomial basis and boundary conditions are known, can be recovered using Total Variation norm minimization. The proof of the uniqueness of the solution uses the method of ‘dual’ interpolating polynomials and is based on Candès and Fernandez-Granda (2014), where the theory was developed for trigonometric polynomials. We also show results for the multivariate case.

A COMPRESSIVE SENSING SIGNAL DETECTION FOR UWB RADAR

A major challenge in UWB signal processing is the requirement for very high sampling rate under Shannon-Nyquist sampling theorem which exceeds the current ADC capacity. Radar signal is essentially a delayed and scaled version of the transmitted pulse, determined by sparse parameters such as time delays and amplitudes. A system for sampling UWB radar signal at an ultra- low sampling rate based on the Finite Rate of Innovation (FRI) and the estimation of time delays and amplitudes to detect UWB radar signal is presented in the paper. This sampling scheme which acquires the Fourier series coe-cients often results in sparse parameter extraction for UWB radar signal detection. The parameters such as time-delays and amplitudes are estimated using the total variation norm minimization. With this system, the UWB radar signal can be accurately reconstructed and detected with overwhelming probability at the rate much lower than Nyquist rate. The simulation results show that the proposed approach ofiers very good recovery performances for noisy UWB radar signal using very small number of samples, which is efiective for sampling and detecting UWB radar signal.

Split Bregman Methods and Frame Based Image Restoration

Split Bregman methods introduced in [T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323–343] have been demonstrated to be efficient tools for solving total variation norm minimization problems, which arise from partial differential equation based image restoration such as image denoising and magnetic resonance imaging reconstruction from sparse samples. In this paper, we prove the convergence of the split Bregman iterations, where the number of inner iterations is fixed to be one. Furthermore, we show that these split Bregman iterations can be used to solve minimization problems arising from the analysis based approach for image restoration in the literature. We apply these split Bregman iterations to the analysis based image restoration approach whose analysis operator is derived from tight framelets constructed in [A. Ron and Z. Shen, J. Funct. Anal., 148 (1997), pp. 408–447]. This gives a set of new frame based image restoration algorithms that cover several topics in image restorations...

Total variation regulated EM algorithm [SPECT reconstruction

An iterative Bayesian reconstruction algorithm based on the total variation (TV) norm constraint is proposed. The motivation for using TV regularization is that it is extremely effective for recovering edges of images. This paper extends the TV norm minimization constraint to the field of SPECT image reconstruction with a Poisson noise model. The regularization norm is included in the OSL-EM (one step late expectation maximization) algorithm. Unlike many other edge-preserving regularization techniques, the TV based method depends one parameter. Reconstructions of computer simulations and patient data show that the proposed algorithm has the capacity to smooth noise and maintain sharp edges without introducing over/under shoots and ripples around the edges.