Sparse MRI and CT Reconstruction

Sparse signal reconstruction is of the utmost importance for efficient medical imaging, conducting accurate screening for security and inspection, and for non-destructive testing. The sparsity of the signal is dictated by either feasibility, or the cost and the screening time constraints of the system. In this work, two major sparse signal reconstruction systems such as compressed sensing magnetic resonance imaging (MRI) and sparse-view computed tomography (CT) are investigated. For medical CT, a limited number of views (sparse-view) is an option for whether reducing the amount of ionizing radiation or the screening time and the cost of the procedure. In applications such as non-destructive testing or inspection of large objects, like a cargo container, one angular view can take up to a few minutes for only one slice. On the other hand, some views can be unavailable due to the configuration of the system. A problem of data sufficiency and on how to estimate a tomographic image when the projection data are not ideally sufficient for precise reconstruction is one of two major objectives of this work. Three CT reconstruction methods are proposed: algebraic iterative reconstruction-reprojection (AIRR), sparse-view CT reconstruction based on curvelet and total variation regularization (CTV), and sparse-view CT reconstruction based on nonconvex L1-L2 regularization. The experimental results confirm a high performance based on subjective and objective quality metrics. Additionally, sparse-view neutron-photon tomography is studied based on Monte-Carlo modelling to demonstrate shape reconstruction, material discrimination and visualization based on the proposed 3D object reconstruction method and material discrimination signatures. One of the methods for efficient acquisition of multidimensional signals is the compressed sensing (CS). A significantly low number of measurements can be obtained in different ways, and one is undersampling, that is sampling below the Shannon-Nyquist limit. Magnetic resonance imaging (MRI) suffers inherently from its slow data acquisition. The compressed sensing MRI (CSMRI) offers significant scan time reduction with advantages for patients and health care economics. In this work, three frameworks are proposed and evaluated, i.e., CSMRI based on curvelet transform and total generalized variation (CT-TGV), CSMRI using curvelet sparsity and nonlocal total variation: CS-NLTV, CSMRI that explores shearlet sparsity and nonlocal total variation: SS-NLTV. The proposed methods are evaluated experimentally and compared to the previously reported state-of-the-art methods. Results demonstrate a significant improvement of image reconstruction quality on different medical MRI datasets

08492 Abstracts Collection -- Structured Decompositions and Efficient Algorithms

From 30.11. to 05.12.2008, the Dagstuhl Seminar 08492 ``Structured Decompositions and Efficient Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Optimal sparsity allows reliable system-aware restoration of fluorescence microscopy images

Incluye: artículo, material suplementario, videos y software.Fluorescence microscopy is one of the most indispensable and informative driving forces for biological research, but the extent of observable biological phenomena is essentially determined by the content and quality of the acquired images. To address the different noise sources that can degrade these images, we introduce an algorithm for multiscale image restoration through optimally sparse representation (MIRO). MIRO is a deterministic framework that models the acquisition process and uses pixelwise noise correction to improve image quality. Our study demonstrates that this approach yields a remarkable restoration of the fluorescence signal for a wide range of microscopy systems, regardless of the detector used (e.g., electron-multiplying charge-coupled device, scientific complementary metal-oxide semiconductor, or photomultiplier tube). MIRO improves current imaging capabilities, enabling fast, low-light optical microscopy, accurate image analysis, and robust machine intelligence when integrated with deep neural networks. This expands the range of biological knowledge that can be obtained from fluorescence microscopy.We acknowledge the support of the National Institutes of Health grants R35GM124846 (to S.J.) and R01AA028527 (to C.X.), the National Science Foundation grants BIO2145235 and EFMA1830941 (to S.J.), and Marvin H. and Nita S. Floyd Research Fund (to S.J.). This research project was supported, in part, by the Emory University Integrated Cellular Imaging Microscopy Core and by PHS Grant UL1TR000454 from the Clinical and Translational Science Award Program, National Institutes of Health, and National Center for Advancing Translational Sciences.S

An Image Filter Based on Shearlet Transformation and Particle Swarm Optimization Algorithm

Digital image is always polluted by noise and made data postprocessing difficult. To remove noise and preserve detail of image as much as possible, this paper proposed image filter algorithm which combined the merits of Shearlet transformation and particle swarm optimization (PSO) algorithm. Firstly, we use classical Shearlet transform to decompose noised image into many subwavelets under multiscale and multiorientation. Secondly, we gave weighted factor to those subwavelets obtained. Then, using classical Shearlet inverse transform, we obtained a composite image which is composed of those weighted subwavelets. After that, we designed fast and rough evaluation method to evaluate noise level of the new image; by using this method as fitness, we adopted PSO to find the optimal weighted factor we added; after lots of iterations, by the optimal factors and Shearlet inverse transform, we got the best denoised image. Experimental results have shown that proposed algorithm eliminates noise effectively and yields good peak signal noise ratio (PSNR)

Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented