Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics

Assessment of perceptual distortion boundary through applying reversible watermarking to brain MR images

The digital medical workflow faces many circumstances in which the images can be manipulated during viewing, extracting and exchanging. Reversible and imperceptible watermarking approaches have the potential to enhance trust within the medical imaging pipeline through ensuring the authenticity and integrity of the images to confirm that the changes can be detected and tracked. This study concentrates on the imperceptibility issue. Unlike reversibility, for which an objective assessment can be easily made, imperceptibility is a factor of human cognition that needs to be evaluated within the human context. By defining a perceptual boundary of detecting the modification, this study enables the formation of objective guidelines for the method of data encoding and level of image/pixel modification that translates to a specific watermark magnitude. This study implements a relative Visual Grading Analysis (VGA) evaluation of 117 brain MR images (8 original and 109 watermarked), modified by varying techniques and magnitude of image/pixel modification to determine where this perceptual boundary exists and relate the point at which change becomes noticeable to the objective measures of the image fidelity evaluation. The outcomes of the visual assessment were linked to the images Peak Signal to Noise Ratio (PSNR) values, thereby identifying the visual degradation threshold. The results suggest that, for watermarking applications, if a watermark is applied to the 512x512 pixel (16 bpp grayscale) images used in the study, a subsequent assessment of PSNR=82dB or greater would mean that there would be no reason to suspect that the watermark would be visually detectable. Keywords: Medical imaging; DICOM; Reversible Watermarking; Imperceptibility; Image Quality; Visual Grading Analysis

Textural Difference Enhancement based on Image Component Analysis

In this thesis, we propose a novel image enhancement method to magnify the textural differences in the images with respect to human visual characteristics. The method is intended to be a preprocessing step to improve the performance of the texture-based image segmentation algorithms. We propose to calculate the six Tamura's texture features (coarseness, contrast, directionality, line-likeness, regularity and roughness) in novel measurements. Each feature follows its original understanding of the certain texture characteristic, but is measured by some local low-level features, e.g., direction of the local edges, dynamic range of the local pixel intensities, kurtosis and skewness of the local image histogram. A discriminant texture feature selection method based on principal component analysis (PCA) is then proposed to find the most representative characteristics in describing textual differences in the image. We decompose the image into pairwise components representing the texture characteristics strongly and weakly, respectively. A set of wavelet-based soft thresholding methods are proposed as the dictionaries of morphological component analysis (MCA) to sparsely highlight the characteristics strongly and weakly from the image. The wavelet-based thresholding methods are proposed in pair, therefore each of the resulted pairwise components can exhibit one certain characteristic either strongly or weakly. We propose various wavelet-based manipulation methods to enhance the components separately. For each component representing a certain texture characteristic, a non-linear function is proposed to manipulate the wavelet coefficients of the component so that the component is enhanced with the corresponding characteristic accentuated independently while having little effect on other characteristics. Furthermore, the above three methods are combined into a uniform framework of image enhancement. Firstly, the texture characteristics differentiating different textures in the image are found. Secondly, the image is decomposed into components exhibiting these texture characteristics respectively. Thirdly, each component is manipulated to accentuate the corresponding texture characteristics exhibited there. After re-combining these manipulated components, the image is enhanced with the textural differences magnified with respect to the selected texture characteristics. The proposed textural differences enhancement method is used prior to both grayscale and colour image segmentation algorithms. The convincing results of improving the performance of different segmentation algorithms prove the potential of the proposed textural difference enhancement method

Textural Difference Enhancement based on Image Component Analysis

In this thesis, we propose a novel image enhancement method to magnify the textural differences in the images with respect to human visual characteristics. The method is intended to be a preprocessing step to improve the performance of the texture-based image segmentation algorithms. We propose to calculate the six Tamura's texture features (coarseness, contrast, directionality, line-likeness, regularity and roughness) in novel measurements. Each feature follows its original understanding of the certain texture characteristic, but is measured by some local low-level features, e.g., direction of the local edges, dynamic range of the local pixel intensities, kurtosis and skewness of the local image histogram. A discriminant texture feature selection method based on principal component analysis (PCA) is then proposed to find the most representative characteristics in describing textual differences in the image. We decompose the image into pairwise components representing the texture characteristics strongly and weakly, respectively. A set of wavelet-based soft thresholding methods are proposed as the dictionaries of morphological component analysis (MCA) to sparsely highlight the characteristics strongly and weakly from the image. The wavelet-based thresholding methods are proposed in pair, therefore each of the resulted pairwise components can exhibit one certain characteristic either strongly or weakly. We propose various wavelet-based manipulation methods to enhance the components separately. For each component representing a certain texture characteristic, a non-linear function is proposed to manipulate the wavelet coefficients of the component so that the component is enhanced with the corresponding characteristic accentuated independently while having little effect on other characteristics. Furthermore, the above three methods are combined into a uniform framework of image enhancement. Firstly, the texture characteristics differentiating different textures in the image are found. Secondly, the image is decomposed into components exhibiting these texture characteristics respectively. Thirdly, each component is manipulated to accentuate the corresponding texture characteristics exhibited there. After re-combining these manipulated components, the image is enhanced with the textural differences magnified with respect to the selected texture characteristics. The proposed textural differences enhancement method is used prior to both grayscale and colour image segmentation algorithms. The convincing results of improving the performance of different segmentation algorithms prove the potential of the proposed textural difference enhancement method

Gated frequency-resolved optical imaging with an optical parametric amplifier for medical applications

Implementation of optical imagery in a diffuse inhomogeneous medium such as biological tissue requires an understanding of photon migration and multiple scattering processes which act to randomize pathlength and degrade image quality. The nature of transmitted light from soft tissue ranges from the quasi-coherent properties of the minimally scattered component to the random incoherent light of the diffuse component. Recent experimental approaches have emphasized dynamic path-sensitive imaging measurements with either ultrashort laser pulses (ballistic photons) or amplitude modulated laser light launched into tissue (photon density waves) to increase image resolution and transmissive penetration depth. Ballistic imaging seeks to compensate for these {open_quotes}fog-like{close_quotes} effects by temporally isolating the weak early-arriving image-bearing component from the diffusely scattered background using a subpicosecond optical gate superimposed on the transmitted photon time-of-flight distribution. The authors have developed a broadly wavelength tunable (470 nm -2.4 {mu}m), ultrashort amplifying optical gate for transillumination spectral imaging based on optical parametric amplification in a nonlinear crystal. The time-gated image amplification process exhibits low noise and high sensitivity, with gains greater than 104 achievable for low light levels. We report preliminary benchmark experiments in which this system was used to reconstruct, spectrally upcovert, and enhance near-infrared two-dimensional images with feature sizes of 65 {mu}m/mm{sup 2} in background optical attenuations exceeding 10{sup 12}. Phase images of test objects exhibiting both absorptive contrast and diffuse scatter were acquired using a self-referencing Shack-Hartmann wavefront sensor in combination with short-pulse quasi-ballistic gating. The sensor employed a lenslet array based on binary optics technology and was sensitive to optical path distortions approaching {lambda}/100

Wavefront shaping approaches for spectral domain optical coherence tomography

Optical coherence tomography (OCT) enables sub-surface three dimensional imaging with micrometer resolution. The technique is based on the time-of-flight gated detection of light which is backscattered from a sample and has applications in non-destructive testing, metrology and contact-less and non-invasive medical diagnostics. With scattering media such as the human skin, the penetration depth is limited to just a few millimetres, on the other hand, and OCT imaging hence allows to investigate superficial sample layers only. Scattering of light is a deterministic process. As a consequence, manipulation of the beam incident to a turbid sample yields control over the scattered field. Following this approach, a number of groups demonstrated iterative wavefront optimization algorithms to be able to focus light transmitted through or backscattered from opaque media. First applications to optical coherence tomography were shown to extend the penetration depth as well as to improve the signal-to-noise ratio when imaging biological tissue. This work explores practical approaches to combine wavefront shaping techniques with OCT imaging. To this end, a compact spectral domain (SD-) OCT design is developed which enables single-pass and independent wavefront control at the reference and at sample beam. Iterative optimization of the phase pattern applied to the sample beam is shown to selectively enhance the amplitude of the OCT signal received from scattering media. In a more sophisticated approach, the acquisition of the time-resolved reflection matrix, which yields the linear dependence of the OCT signal on the field at the sample beam, is demonstrated. Subsequent wavefront optimization based on a phase conjugation algorithm is shown to enhance the OCT signal but not image artefacts, even though no attempt is made to actively suppress these artefacts. The approach is comparable to iterative wavefront optimization but yields a substantially improved acquisition speed. First imaging applications demonstrate the algorithm to enhance the signal-to-noise ratio and the penetration depth with scattering media, such as biological tissue, and to reduce the observed speckle contrast, similar to compounding algorithms. Furthermore, the acquisition of the reflection matrix and subsequent signal enhancement based on binary amplitude-only (on/off) beam shaping is presented for the first time. The technique can be implemented with digital micromirror devices which enable high-speed implementations. The presented techniques constitute substantial improvements compared to previous works and yield promising results in the context of depth-enhanced OCT imaging with scattering biological tissue. Approaches to further enhance the performance and the acquisition speed for real-time in-vivo imaging applications are discussed.Niedersächsisches Ministerium für Wissenschaft und Kultur (MWK)/Tailored Light/78904-63-6/16/E

Supercontinuum in the practice of Optical Coherence Tomography with emphasis on noise effects

Optical Coherence Tomography (OCT) is an imaging modality which has proven, since the early 1990s, its incredible potential. Nowadays, numerous fields of medical investigation, such as Ophthalmology, Dermatology or Cardiovascular imaging, would not be the same without the diagnostic tools bring by OCT. This tremendous development has been supported by industry support through improvement of dedicated components such as lasers, cameras and optics. A great example of this development is the evolution of Supercontinuum (SC) sources. Due to the extremely broad spectrum cover by SC sources, their high power density and high spatial coherence, it seems obvious to use them for driving OCT systems. However, an intensity noise issue arising from the SC sources has been reported as a limitation for OCT and needs to be addressed. The aim of the work presented in this thesis is to create a link between the world of Optical Coherence Tomography and Supercontinuum physics in order to understand the origins and the impact of SC source intensity noise into the OCT systems. This work is of importance as it helps to optimize the usefulness of the current generation of SC sources. Also, this work is a part of the work necessary for developing a new generation of SC sources which completely addresses the intensity noise limitations. More precisely, a part of the work presented deals with an optimization of the association SC source and OCT. The second part of the results is an attempt for improving this association by using a new SC source design

Identification of corneal mechanical properties using optical tomography and digital volume correlation

This work presents an effective methodology for measuring the depth-resolved 3D full-field deformation of semitransparent, light scattering soft tissues such as vertebrate eye cornea. This was obtained by performing digital volume correlation on optical coherence tomography volume reconstructions of silicone rubber phantoms and porcine cornea samples. Both the strip tensile tests and the posterior inflation tests have been studied. Prior to these tests, noise effect and strain induced speckle decorrelation were first studied using experimental and simulation methods. The interpolation bias in the strain results has also been analyzed. Two effective approaches have been introduced to reduce the interpolation bias. To extract material constitutive parameters from the 3D full-field deformation measurements, the virtual fields method has been extended into 3D. Both manually defined virtual fields and the optimized piecewise virtual fields have been developed and compared with each other. Efforts have also been made in developing a method to correct the refraction induced distortions in the optical coherence tomography reconstructions. Tilt tests of different silicone rubber phantoms have been implemented to evaluate the performance of the refraction correction method in correcting the distorted reconstructions