Projected Newton Method for noise constrained Tikhonov regularization

Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy principle. However, most approaches require the solution of the Tikhonov problem for many different values of the regularization parameter, which is computationally demanding for large scale problems. We propose a new and efficient algorithm which simultaneously solves the Tikhonov problem and finds the corresponding regularization parameter such that the discrepancy principle is satisfied. We achieve this by formulating the problem as a nonlinear system of equations and solving this system using a line search method. We obtain a good search direction by projecting the problem onto a low dimensional Krylov subspace and computing the Newton direction for the projected problem. This projected Newton direction, which is significantly less computationally expensive to calculate than the true Newton direction, is then combined with a backtracking line search to obtain a globally convergent algorithm, which we refer to as the Projected Newton method. We prove convergence of the algorithm and illustrate the improved performance over current state-of-the-art solvers with some numerical experiments

A new Edge Detector Based on Parametric Surface Model: Regression Surface Descriptor

In this paper we present a new methodology for edge detection in digital images. The first originality of the proposed method is to consider image content as a parametric surface. Then, an original parametric local model of this surface representing image content is proposed. The few parameters involved in the proposed model are shown to be very sensitive to discontinuities in surface which correspond to edges in image content. This naturally leads to the design of an efficient edge detector. Moreover, a thorough analysis of the proposed model also allows us to explain how these parameters can be used to obtain edge descriptors such as orientations and curvatures. In practice, the proposed methodology offers two main advantages. First, it has high customization possibilities in order to be adjusted to a wide range of different problems, from coarse to fine scale edge detection. Second, it is very robust to blurring process and additive noise. Numerical results are presented to emphasis these properties and to confirm efficiency of the proposed method through a comparative study with other edge detectors.Comment: 21 pages, 13 figures and 2 table

Development Of A High Performance Mosaicing And Super-Resolution Algorithm

In this dissertation, a high-performance mosaicing and super-resolution algorithm is described. The scale invariant feature transform (SIFT)-based mosaicing algorithm builds an initial mosaic which is iteratively updated by the robust super resolution algorithm to achieve the final high-resolution mosaic. Two different types of datasets are used for testing: high altitude balloon data and unmanned aerial vehicle data. To evaluate our algorithm, five performance metrics are employed: mean square error, peak signal to noise ratio, singular value decomposition, slope of reciprocal singular value curve, and cumulative probability of blur detection. Extensive testing shows that the proposed algorithm is effective in improving the captured aerial data and the performance metrics are accurate in quantifying the evaluation of the algorithm

Plant Seed Identification

Plant seed identification is routinely performed for seed certification in seed trade, phytosanitary certification for the import and export of agricultural commodities, and regulatory monitoring, surveillance, and enforcement. Current identification is performed manually by seed analysts with limited aiding tools. Extensive expertise and time is required, especially for small, morphologically similar seeds. Computers are, however, especially good at recognizing subtle differences that humans find difficult to perceive. In this thesis, a 2D, image-based computer-assisted approach is proposed. The size of plant seeds is extremely small compared with daily objects. The microscopic images of plant seeds are usually degraded by defocus blur due to the high magnification of the imaging equipment. It is necessary and beneficial to differentiate the in-focus and blurred regions given that only sharp regions carry distinctive information usually for identification. If the object of interest, the plant seed in this case, is in- focus under a single image frame, the amount of defocus blur can be employed as a cue to separate the object and the cluttered background. If the defocus blur is too strong to obscure the object itself, sharp regions of multiple image frames acquired at different focal distance can be merged together to make an all-in-focus image. This thesis describes a novel non-reference sharpness metric which exploits the distribution difference of uniform LBP patterns in blurred and non-blurred image regions. It runs in realtime on a single core cpu and responses much better on low contrast sharp regions than the competitor metrics. Its benefits are shown both in defocus segmentation and focal stacking. With the obtained all-in-focus seed image, a scale-wise pooling method is proposed to construct its feature representation. Since the imaging settings in lab testing are well constrained, the seed objects in the acquired image can be assumed to have measureable scale and controllable scale variance. The proposed method utilizes real pixel scale information and allows for accurate comparison of seeds across scales. By cross-validation on our high quality seed image dataset, better identification rate (95%) was achieved compared with pre- trained convolutional-neural-network-based models (93.6%). It offers an alternative method for image based identification with all-in-focus object images of limited scale variance. The very first digital seed identification tool of its kind was built and deployed for test in the seed laboratory of Canadian food inspection agency (CFIA). The proposed focal stacking algorithm was employed to create all-in-focus images, whereas scale-wise pooling feature representation was used as the image signature. Throughput, workload, and identification rate were evaluated and seed analysts reported significantly lower mental demand (p = 0.00245) when using the provided tool compared with manual identification. Although the identification rate in practical test is only around 50%, I have demonstrated common mistakes that have been made in the imaging process and possible ways to deploy the tool to improve the recognition rate

A portable EIT system for emergency medical care

Electrical Impedance Tomography (EIT) is a medical imaging technique in which images of tissue conductivity within a body can be inferred from surface electrode measurements. The main goal of this study is to develop a portable EIT system incorporating an optimized electrode layout to detect intracranial haematomas for use in emergency care. A growing haematoma can cause severe and even permanent damage to the delicate tissue of the brain, morbidity, and eventual death of the patient. No capability is at present available for the diagnosis of haematomas pre-hospitalisation or by first-responders. The lack of this crucial information can lead to bad decisions on patient management, and in particular, where to send the patient. Blood has a high electrical conductivity contrast relative to other cranial tissue and can be detected and monitored using electrical impedance methods. EIT is a non-invasive, low-cost monitoring alternative to other imaging modalities, and has the potential to detect bleeding and to localize the approximate bleeding site. A device of this nature would reduce treatment delays, save on costs and waste, and most significantly, positively impact patient outcomes. The first step was a numerical simulation study on FE models. The full array and the hemi-array electrode layouts were modelled and the anomalies were simulated in different positions with different sizes. The results were obtained using TSVD and WMNM reconstruction methods by COMSOL linked with MATLAB. The simulated anomalies were detected for all the positions using both layouts; however those from the full array were in general superior to the hemi-array. In order to perform realistic experiments, a prototype EIT system was constructed in the laboratory. The constructed EIT has 16 channels and operates in the frequency range of 10 kHz to 100 kHz with a temporal resolution of 100 frames per second and high level of accuracy of 93.5 %. The minimum number of 8 electrodes was chosen in this study for emergency care. Minimizing the number of electrodes speeds up the electrode setup process and avoids the need to move the patient s head in emergency care. In the second part of this study, phantom experiments were performed to find an optimised electrode layout for emergency care. The full array and the hemi-array were investigated using phantom experiments. As expected, the full array layout had the best performance in general; however, the performance of the hemi-array layout was very poor. Thus a novel optimised electrode layout (semi-array) for emergency care was proposed and evaluated in phantom experiments. For the hemi-array and the semi-array layouts, measurement sensitivity depends strongly on the anomaly location since the electrodes are not placed all over the head. The HA layout performed very badly, with the best radial localization error of 0.8100 mm, compared to the SA layout with the worst error of 0.2486 mm. Some reconstructed anomalies located far from the electrodes in the posterior region were almost invisible or erroneous for the hemi-array layout; however, it is enhanced by using the semi-array layout. Finally, in vitro experiments were conducted on ovine models. In most of the experiments carried out by other researchers, since the location of the simulated anomalies was not known and the simulated blood was normally injected into the body or the head, localization of the anomalies was not considered and the quantity of the injected blood was investigated solely. In our new method of experiment, the position of the anomalies was known a priori and thus could be compared accurately to the EIT results. The full array and the semi-array layouts were compared in terms of detection, localisation and size estimation of haematomas. As expected, the full array layout was found to be more robust than the semi-array layout with the best mean value of the localization error of 0.0564 mm and the worst QI error of around 30%. Using a minimum number of electrodes in an optimised layout is always desirable in clinical applications. The semi-array 8-electrode layout prevents unnecessary movements and the electrode connections to the head would be very quick in emergency care. Although the semi-array 8-electrode layout reduced the sensitivity of the measurements, the findings from the experiments indicated its potential to detect and monitor haematomas and probably extend its application for emergency applications where the required accuracy is not critical