Medical Image Denoising Using Mixed Transforms

يقترح في هذا البحث طريقة تعتمد على خليط من التحويلات Wavelet Transform(WT) و Multiwavelet Transform (MWT) من اجل تقليل التشوه في الصور الطبية . تعتمد الطريقة المقترحة على استخدام WT  و MWT بالتعاقب لتعزيز اداء ازالة التشوه من الصور الطبية. عمليا , يتم في البداية اضافة تشويه لصور الرنين المغناطيسي (MRI) والتصوير المقطعي المحوسب (CT)  من اجل الاختبار. ثم تعالج الصورة المشوهة بواسطة WT  لتنتج اربع تقسيمات للصورة موزعة على اساس التردد ويعالج كل تقسيم بواسطة MWT  قبل مرحلة ازالة التشوه المكثفة او البسيطة. اوضحت النتائج العملية ان نسبة الاشارة الى الضوضاء (PSNR) تحسنت بشكل ملحوظ وتم المحافظة على المعلومات الاساسية للصورة. بالاضافة الى ذلك, فان متوسط نسبة الخطا انخفض تبعا لذلك بالمقارنة مع الطرق الاخرى. In this paper,  a mixed transform method is proposed based on a combination of wavelet transform (WT) and multiwavelet transform (MWT) in order to denoise medical images. The proposed method consists of WT and MWT in cascade form to enhance the denoising performance of image processing. Practically, the first step is to add a noise to Magnetic Resonance Image (MRI) or Computed Tomography (CT) images for the sake of testing. The noisy image is processed by WT to achieve four sub-bands and each sub-band is treated individually using MWT before the soft/hard denoising stage. Simulation results show that a high peak signal to noise ratio (PSNR) is improved significantly and the characteristic features are well preserved by employing mixed transform of WT and MWT due to their capability of separating noise signals from image signals. Moreover, the corresponding mean square error (MSE) is decreased accordingly compared to other available methods

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github

Edge-Aware Extended Star-Tetrix Transforms for CFA-Sampled Raw Camera Image Compression

Codecs using spectral-spatial transforms efficiently compress raw camera images captured with a color filter array (CFA-sampled raw images) by changing their RGB color space into a decorrelated color space. This study describes two types of spectral-spatial transform, called extended Star-Tetrix transforms (XSTTs), and their edge-aware versions, called edge-aware XSTTs (EXSTTs), with no extra bits (side information) and little extra complexity. They are obtained by (i) extending the Star-Tetrix transform (STT), which is one of the latest spectral-spatial transforms, to a new version of our previously proposed wavelet-based spectral-spatial transform and a simpler version, (ii) considering that each 2-D predict step of the wavelet transform is a combination of two 1-D diagonal or horizontal-vertical transforms, and (iii) weighting the transforms along the edge directions in the images. Compared with XSTTs, the EXSTTs can decorrelate CFA-sampled raw images well: they reduce the difference in energy between the two green components by about $3.38$--$30.08$ \% for high-quality camera images and $8.97$--$14.47$ \% for mobile phone images. The experiments on JPEG 2000-based lossless and lossy compression of CFA-sampled raw images show better performance than conventional methods. For high-quality camera images, the XSTTs/EXSTTs produce results equal to or better than the conventional methods: especially for images with many edges, the type-I EXSTT improves them by about $0.03$--$0.19$ bpp in average lossless bitrate and the XSTTs improve them by about $0.16$--$0.96$ dB in average Bj\o ntegaard delta peak signal-to-noise ratio. For mobile phone images, our previous work perform the best, whereas the XSTTs/EXSTTs show similar trends to the case of high-quality camera images

A nonlinear Stein based estimator for multichannel image denoising

The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Stein's principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising technique

Locally Adaptive Wavelet-Based Image Interpolation

We describe a spatially adaptive algorithm for image interpolation. The algorithm uses a wavelet transform to extract information about sharp variations in the low-resolution image and then implicitly applies interpolation which adapts to the image local smoothness/singularity characteristics. The proposed algorithm yields images that are sharper compared to several other methods that we have considered in this paper. Better performance comes at the expense of higher complexity

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

A Computational Framework for the Structural Change Analysis of 3D Volumes of Microscopic Specimens

Glaucoma, commonly observed with an elevation in the intraocular pressure level (IOP), is one of the leading causes of blindness. The lamina cribrosa is a mesh-like structure that provides axonal support for the optic nerves leaving the eye. The changes in the laminar structure under IOP elevations may result in the deaths of retinal ganglion cells, leading to vision degradation and loss. We have developed a comprehensive computational framework that can assist the study of structural changes in microscopic structures such as lamina cribrosa. The optical sectioning property of a confocal microscope facilitates imaging thick microscopic specimen at various depths without physical sectioning. The confocal microscope images are referred to as optical sections. The computational framework developed includes: 1) a multi-threaded system architecture for tracking a volume-of-interest within a microscopic specimen in a parallel computation environment using a reliable-multicast for collective-communication operations 2) a Karhunen-Loève (KL) expansion based adaptive noise prefilter for the restoration of the optical sections using an inverse restoration method 3) a morphological operator based ringing metric to quantify the ringing artifacts introduced during iterative restoration of optical sections 4) a l2 norm based error metric to evaluate the performance of optical flow algorithms without a priori knowledge of the true motion field and 5) a Compute-and-Propagate (CNP) framework for iterative optical flow algorithms. The realtime tracking architecture can convert a 2D-confocal microscope into a 4D-confocal microscope with tracking. The adaptive KL filter is suitable for realtime restoration of optical sections. The CNP framework significantly improves the speed and convergence of the iterative optical flow algorithms. Also, the CNP framework can reduce the errors in the motion field estimates due to the aperture problem. The performance of the proposed framework is demonstrated on real-life image sequences and on z-Stack datasets of random cotton fibers and lamina cribrosa of a cow retina with an experimentally induced glaucoma. The proposed framework can be used for routine laboratory and clinical investigation of microstructures such as cells and tissues, for the evaluation of complex structures such as cornea and has potential use as a surgical guidance tool

Non-local methods for InSAR parameters estimation

In the thesis work the nonlocal paradigm has been investigated in the framework of Multitemporal SAR Interferometry, e.g. Differential Interferometry, Tomography, etc., and single InSAR pair, e.g. DEM generation. In the former, Adaptive Multi-Looking methods have been developed for the generation of interferometric data-stacks. Following the nonlocal approach, the proposed methods rely only on similar pixels according to a suitable similarity measure that exploits the stack's temporal information. An hybrid approach that jointly uses the nonlocal paradigm and transform domain filtering has been investigated for InSAR pair phase estimation. On the track of the BM3D and SARBM3D algorithms, different approaches to the filtering in the transform domain are investigated. Furthermore, a novel approach to the similarity computation and filtering, based on a relative-topography content of the interferometric phase rather than its absolute value, is proposed

Use of Pattern Classification Algorithms to Interpret Passive and Active Data Streams from a Walking-Speed Robotic Sensor Platform

In order to perform useful tasks for us, robots must have the ability to notice, recognize, and respond to objects and events in their environment. This requires the acquisition and synthesis of information from a variety of sensors. Here we investigate the performance of a number of sensor modalities in an unstructured outdoor environment, including the Microsoft Kinect, thermal infrared camera, and coffee can radar. Special attention is given to acoustic echolocation measurements of approaching vehicles, where an acoustic parametric array propagates an audible signal to the oncoming target and the Kinect microphone array records the reflected backscattered signal. Although useful information about the target is hidden inside the noisy time domain measurements, the Dynamic Wavelet Fingerprint process (DWFP) is used to create a time-frequency representation of the data. A small-dimensional feature vector is created for each measurement using an intelligent feature selection process for use in statistical pattern classification routines. Using our experimentally measured data from real vehicles at 50 m, this process is able to correctly classify vehicles into one of five classes with 94% accuracy. Fully three-dimensional simulations allow us to study the nonlinear beam propagation and interaction with real-world targets to improve classification results