Anisotropic Total Variation Regularized L^1-Approximation and Denoising/Deblurring of 2D Bar Codes

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.Comment: 34 pages, 6 figures (with a total of 30 subfigures); errors corrected in Version 3, see Errata 1.1, 4.4, and 6.6 (v3 numbering) for more informatio

A regularization approach to blind deblurring and denoising of QR barcodes

QR bar codes are prototypical images for which part of the image is a priori known (required patterns). Open source bar code readers, such as ZBar, are readily available. We exploit both these facts to provide and assess purely regularization-based methods for blind deblurring of QR bar codes in the presence of noise

A Regularization Approach to Blind Deblurring and Denoising of QR Barcodes

QR bar codes are prototypical images for which part of the image is a priori known (required patterns). Open source bar code readers, such as ZBar, are readily available. We exploit both these facts to provide and assess purely regularization-based methods for blind deblurring of QR bar codes in the presence of noise.Comment: 14 pages, 19 figures (with a total of 57 subfigures), 1 table; v3: previously missing reference [35] adde

Fast restoration for out-of-focus blurred images of QR code with edge prior information via image sensing.

Out-of-focus blurring of the QR code is very common in mobile Internet systems, which often causes failure of authentication as a result of a misreading of the information hence adversely affects the operation of the system. To tackle this difficulty, this work firstly introduced an edge prior information, which is the average distance between the center point and the edge of the clear QR code images in the same batch. It is motivated by the theoretical analysis and the practical observation of the theory of CMOS image sensing, optics information, blur invariants, and the invariance of the center of the diffuse light spots. After obtaining the edge prior information, combining the iterative image and the center point of the binary image, the proposed method can accurately estimate the parameter of the out-of-focus blur kernel. Furthermore, we obtain the sharp image by Wiener filter, a non-blind image deblurring algorithm. By this, it avoids excessive redundant calculations. Experimental results validate that the proposed method has great practical utility in terms of deblurring quality, robustness, and computational efficiency, which is suitable for barcode application systems, e.g., warehouse, logistics, and automated production

Total variation denoising in l1l^1 anisotropy

We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a naturally defined class of functions piecewise constant on rectangles (PCR). This class forms a strictly dense subset of the space of functions of bounded variation with an anisotropic norm. The main result shows that if the given noisy image is a PCR function, then solutions to both considered problems also have this property. For PCR data the problem of finding the solution is reduced to a finite algorithm. We discuss some implications of this result, for instance we use it to prove that continuity is preserved by both considered problems.Comment: 34 pages, 9 figure

VARIATIONAL METHODS FOR IMAGE DEBLURRING AND DISCRETIZED PICARD\u27S METHOD

In this digital age, it is more important than ever to have good methods for processing images. We focus on the removal of blur from a captured image, which is called the image deblurring problem. In particular, we make no assumptions about the blur itself, which is called a blind deconvolution. We approach the problem by miniming an energy functional that utilizes total variation norm and a fidelity constraint. In particular, we extend the work of Chan and Wong to use a reference image in the computation. Using the shock filter as a reference image, we produce a superior result compared to existing methods. We are able to produce good results on non-black background images and images where the blurring function is not centro-symmetric. We consider using a general Lp norm for the fidelity term and compare different values for p. Using an analysis similar to Strong and Chan, we derive an adaptive scale method for the recovery of the blurring function. We also consider two numerical methods in this disseration. The first method is an extension of Picards method for PDEs in the discrete case. We compare the results to the analytical Picard method, showing the only difference is the use of the approximation versus exact derivatives. We relate the method to existing finite difference schemes, including the Lax-Wendroff method. We derive the stability constraints for several linear problems and illustrate the stability region is increasing. We conclude by showing several examples of the method and how the computational savings is substantial. The second method we consider is a black-box implementation of a method for solving the generalized eigenvalue problem. By utilizing the work of Golub and Ye, we implement a routine which is robust against existing methods. We compare this routine against JDQZ and LOBPCG and show this method performs well in numerical testing

Change Point Estimation of Bilevel Functions

Reconstruction of a bilevel function such as a bar code signal in a partially blind deconvolution problem is an important task in industrial processes. Existing methods are based on either the local approach or the regularization approach with a total variation penalty. This article reformulated the problem explicitly in terms of change points of the 0-1 step function. The bilevel function is then reconstructed by solving the nonlinear least squares problem subject to linear inequality constraints, with starting values provided by the local extremas of the derivative of the convolved signal from discrete noisy data. Simulation results show a considerable improvement of the quality of the bilevel function using the proposed hybrid approach over the local approach. The hybrid approach extends the workable range of the standard deviation of the Gaussian kernel significantly

Total Variation Based Restoration of Bilevel Waveforms

A series of Total Variation based algorithms are presented for the restoration of bilevel waveforms from observed signals. The proposed model is discussed analytically and numerically via the gradient descent minimization of the TV energy. The application of restoration of bilevel waveforms encoded within barcode images is presented. A super- resolution technique is proposed as a reduction of dimensionality of the image data. The result is a high resolution image from which the encoded bilevel waveform is restored. Implementation of results is shown for synthetic and real images