Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDeblurring of One Dimensional Bar Codes via Total Variation Energy Minimisation
118
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Using total variation based energy minimisation we address the recovery of a blurred (convoluted) one dimensional (1D) barcode. We consider functionals defined over all possible barcodes with fidelity to a convoluted signal of a barcode, and regularised by total variation. Our fidelity terms consist of the L^2 distance either directly to the measured signal or preceded by deconvolution. Key length scales and parameters are the X-dimension of the underlying barcode, the size of the supports of the convolution and deconvolution kernels, and the fidelity parameter. For all functionals, we establish regimes (sufficient conditions) wherein the underlying barcode is the unique minimiser. We also present some numerical experiments suggesting that these sufficient conditions are not optimal and the energy methods are quite robust for significant blurring.
rate research
Read More
We consider variations of the Rudin-Osher-Fatemi functional which are particularly well-suited to denoising and deblurring of 2D bar codes. These functionals consist of an anisotropic total variation favoring rectangles and a fidelity term which measure the L^1 distance to the signal, both with and without the presence of a deconvolution operator. Based upon the existence of a certain associated vector field, we find necessary and sufficient conditions for a function to be a minimizer. We apply these results to 2D bar codes to find explicit regimes ---in terms of the fidelity parameter and smallest length scale of the bar codes--- for which a perfect bar code is recoverable via minimization of the functionals. Via a discretization reformulated as a linear program, we perform numerical experiments for all functionals demonstrating their denoising and deblurring capabilities.
We investigate the improvements in Shack-Hartmann wavefront sensor image processing that can be realised using total variation minimisation techniques to remove noise from these images. We perform Monte-Carlo simulation to demonstrate that at certain signal-to-noise levels, sensitivity improvements of up to one astronomical magnitude can be realised. We also present on-sky measurements taken with the CANARY adaptive optics system that demonstrate an improvement in performance when this technique is employed, and show that this algorithm can be implemented in a real-time control system. We conclude that total variation minimisation can lead to improvements in sensitivity of up to one astronomical magnitude when used with adaptive optics systems.
In this paper we study the Total Variation Flow (TVF) in metric random walk spaces, which unifies into a broad framework the TVF on locally finite weighted connected graphs, the TVF determined by finite Markov chains and some nonlocal evolution problems. Once the existence and uniqueness of solutions of the TVF has been proved, we study the asymptotic behaviour of those solutions and, with that aim in view, we establish some inequalities of Poincar{e} type. In particular, for finite weighted connected graphs, we show that the solutions reach the average of the initial data in finite time. Furthermore, we introduce the concepts of perimeter and mean curvature for subsets of a metric random walk space and we study the relation between isoperimetric inequalities and Sobolev inequalities. Moreover, we introduce the concepts of Cheeger and calibrable sets in metric random walk spaces and characterize calibrability by using the $1$-Laplacian operator. Finally, we study the eigenvalue problem whereby we give a method to solve the optimal Cheeger cut problem.
We give an existence proof for variational solutions $u$ associated to the total variation flow. Here, the functions being considered are defined on a metric measure space $(mathcal{X}, d, mu)$ satisfying a doubling condition and supporting a Poincare inequality. For such parabolic minimizers that coincide with a time-independent Cauchy-Dirichlet datum $u_0$ on the parabolic boundary of a space-time-cylinder $Omega times (0, T)$ with $Omega subset mathcal{X}$ an open set and $T > 0$, we prove existence in the weak parabolic function space $L^1_w(0, T; mathrm{BV}(Omega))$. In this paper, we generalize results from a previous work by Bogelein, Duzaar and Marcellini by introducing a more abstract notion for $mathrm{BV}$-valued parabolic function spaces. We argue completely on a variational level.
The main result of this small note is a quantified version of the assertion that if u and v solve two nonlinear stochastic heat equations, and if the mutual energy between the initial states of the two stochastic PDEs is small, then the total masses of the two systems are nearly uncorrelated for a very long time. One of the consequences of this fact is that a stochastic heat equation with regular coefficients is a finite system if and only if the initial state is integrable.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
