Combining Total Variation and Nonlocal Means Regularization for Edge Preserving Image Deconvolution

We propose a new edge preserving image deconvolution model by combining total variation and nonlocal means regularization. Natural images exhibit an high degree of redundancy. Using this redundancy, the nonlocal means regularization strategy is a good technique for detail preserving image restoration. In order to further improve the visual quality of the nonlocal means based algorithm, total variation is introduced to the model to better preserve edges. Then an efficient alternating minimization procedure is used to solve the model. Numerical experiments illustrate the effectiveness of the proposed algorithm

A General Proximal Alternating Minimization Method with Application to Nonconvex Nonsmooth 1D Total Variation Denoising

We deal with a class of problems whose objective functions are compositions of nonconvex nonsmooth functions, which has a wide range of applications in signal/image processing. We introduce a new auxiliary variable, and an efficient general proximal alternating minimization algorithm is proposed. This method solves a class of nonconvex nonsmooth problems through alternating minimization. We give a brilliant systematic analysis to guarantee the convergence of the algorithm. Simulation results and the comparison with two other existing algorithms for 1D total variation denoising validate the efficiency of the proposed approach. The algorithm does contribute to the analysis and applications of a wide class of nonconvex nonsmooth problems

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

Compressed Sensing in the Presence of Side Information

Reconstruction of continuous signals from a number of their discrete samples is central to digital signal processing. Digital devices can only process discrete data and thus processing the continuous signals requires discretization. After discretization, possibility of unique reconstruction of the source signals from their samples is crucial. The classical sampling theory provides bounds on the sampling rate for unique source reconstruction, known as the Nyquist sampling rate. Recently a new sampling scheme, Compressive Sensing (CS), has been formulated for sparse signals. CS is an active area of research in signal processing. It has revolutionized the classical sampling theorems and has provided a new scheme to sample and reconstruct sparse signals uniquely, below Nyquist sampling rates. A signal is called (approximately) sparse when a relatively large number of its elements are (approximately) equal to zero. For the class of sparse signals, sparsity can be viewed as prior information about the source signal. CS has found numerous applications and has improved some image acquisition devices. Interesting instances of CS can happen, when apart from sparsity, side information is available about the source signals. The side information can be about the source structure, distribution, etc. Such cases can be viewed as extensions of the classical CS. In such cases we are interested in incorporating the side information to either improve the quality of the source reconstruction or decrease the number of the required samples for accurate reconstruction. A general CS problem can be transformed to an equivalent optimization problem. In this thesis, a special case of CS with side information about the feasible region of the equivalent optimization problem is studied. It is shown that in such cases uniqueness and stability of the equivalent optimization problem still holds. Then, an efficient reconstruction method is proposed. To demonstrate the practical value of the proposed scheme, the algorithm is applied on two real world applications: image deblurring in optical imaging and surface reconstruction in the gradient field. Experimental results are provided to further investigate and confirm the effectiveness and usefulness of the proposed scheme

Joint methods in imaging based on diffuse image representations

This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics. Simultaneous edge detection and registration of two images: The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped. Detection of grain boundaries from atomic scale images of metals or metal alloys: This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese. Joint motion estimation and restoration of motion-blurred video: A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model. Convexification of the binary Mumford-Shah segmentation model: After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed