SHAPE FROM FOCUS USING LULU OPERATORS AND DISCRETE PULSE TRANSFORM IN THE PRESENCE OF NOISE

A study of three dimension (3D) shape recovery is an interesting and challenging area of research. Recovering the depth information of an object from normal two dimensional (2D) images has been studied for a long time with different techniques. One technique for 3D shape recovery is known as Shape from Focus (SFF). SFF is a method that depends on different focused values in reconstructing the shape, surface, and depth of an object. The different focus values are captured by taking different images for the same object by varying the focus length or varying the distance between object and camera. This single view imaging makes the data gathering simpler in SFF compared to other shape recovery techniques. Calculating the shape of the object using different images with different focused values can be done by applying sharpness detection methods to maximize and detect the focused values. However, noise destroys many information in an image and the result of noise corruption can change the focus values in the images. This thesis presents a new 3D shape recovery technique based on focus values in the presence of noise. The proposed technique is based on LULU operators and Discrete Pulse Transform (DPT). LULU operators are nonlinear rank selector operators that hold consistent separation, total variation and shape preservation properties. The proposed techniques show better and more accurate performance in comparison with the existing SFF techniques in noisy environment

SHAPE FROM FOCUS USING LULU OPERATORS AND DISCRETE PULSE TRANSFORM IN THE PRESENCE OF NOISE

A study of three dimension (3D) shape recovery is an interesting and challenging area of research. Recovering the depth information of an object from normal two dimensional (2D) images has been studied for a long time with different techniques. One technique for 3D shape recovery is known as Shape from Focus (SFF). SFF is a method that depends on different focused values in reconstructing the shape, surface, and depth of an object. The different focus values are captured by taking different images for the same object by varying the focus length or varying the distance between object and camera. This single view imaging makes the data gathering simpler in SFF compared to other shape recovery techniques. Calculating the shape of the object using different images with different focused values can be done by applying sharpness detection methods to maximize and detect the focused values. However, noise destroys many information in an image and the result of noise corruption can change the focus values in the images. This thesis presents a new 3D shape recovery technique based on focus values in the presence of noise. The proposed technique is based on LULU operators and Discrete Pulse Transform (DPT). LULU operators are nonlinear rank selector operators that hold consistent separation, total variation and shape preservation properties. The proposed techniques show better and more accurate performance in comparison with the existing SFF techniques in noisy environment

EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments

We review developments, issues and challenges in Electrical Impedance Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT, Manchester 2003. We focus on the necessity for three dimensional data collection and reconstruction, efficient solution of the forward problem and present and future reconstruction algorithms. We also suggest common pitfalls or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of EIT, Manchester, UK, 200

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

3D differential phase contrast microscopy

We demonstrate 3D phase and absorption recovery from partially coherent intensity images captured with a programmable LED array source. Images are captured through-focus with four different illumination patterns. Using first Born and weak object approximations (WOA), a linear 3D differential phase contrast (DPC) model is derived. The partially coherent transfer functions relate the sample's complex refractive index distribution to intensity measurements at varying defocus. Volumetric reconstruction is achieved by a global FFT-based method, without an intermediate 2D phase retrieval step. Because the illumination is spatially partially coherent, the transverse resolution of the reconstructed field achieves twice the NA of coherent systems and improved axial resolution

Roadmap on optical security

Postprint (author's final draft

Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems

The Application of Preconditioned Alternating Direction Method of Multipliers in Depth from Focal Stack

Post capture refocusing effect in smartphone cameras is achievable by using focal stacks. However, the accuracy of this effect is totally dependent on the combination of the depth layers in the stack. The accuracy of the extended depth of field effect in this application can be improved significantly by computing an accurate depth map which has been an open issue for decades. To tackle this issue, in this paper, a framework is proposed based on Preconditioned Alternating Direction Method of Multipliers (PADMM) for depth from the focal stack and synthetic defocus application. In addition to its ability to provide high structural accuracy and occlusion handling, the optimization function of the proposed method can, in fact, converge faster and better than state of the art methods. The evaluation has been done on 21 sets of focal stacks and the optimization function has been compared against 5 other methods. Preliminary results indicate that the proposed method has a better performance in terms of structural accuracy and optimization in comparison to the current state of the art methods.Comment: 15 pages, 8 figure