Compressed sensing is an emerging approach for signal acquisition wherein theory has shown that a small number of linear, random projection of a signal contains enough information for reconstruction of the signal. Despite its potential to enable lightweight and inexpensive sensing hardware that simultaneously combines signal acquisition and dimensionality reduction, the compressed sensing of images and video still entails several challenges, in particular, a sensing-measurement operator which is difficult to apply in practice due to the heavy memory and computational burdens. Block-based random image sampling coupled with a projection-driven compressed-sensing recovery is proposed to address this challenge. For images, the block-based image acquisition is coupled with reconstruction driven by a directional transform that encourages spatial sparsity. Specifically, both contourlets as well as complex-valued dual-tree wavelets are considered for their highly directional representation, while bivariate shrinkage is adapted to their multiscale decomposition structure to provide the requisite sparsity constraint. Smoothing is achieved via a Wiener filter incorporated into iterative projected Landweber compressed-sensing recovery, yielding fast reconstruction. Also considered is an extension of the basic reconstruction algorithm that incorporates block-based measurements in the domain of a wavelet transform. The pro-posed image recovery algorithm and its extension yield images with quality that matches or exceeds that produced by a popular, yet computationally expensive, technique which minimizes total variation. Additionally, reconstruction quality is substantially superior to that from several prominent pursuits-based algorithms that do not include any smoothing. For video, motion estimation and compensation is utilized to promote temporal sparsity. Because video sequences have temporal redundancy in locations in which objects are moving while the background is still, a residual between the current frame and the previous frame compensated by object motion is shown to be more sparse than the orig-inal frame itself. By using residual reconstruction, information contained in the previous frame contributes to the reconstruction of the current frame. The proposed block-based compressed-sensing reconstruction for video outperforms a simple frame-byrame reconstruction as well as a 3D volumetric reconstruction in terms of visual quality. Finally, quantization of block-based compressed-sensing measurements is considered in order to generate a true bitstream from a compressed-sensing image acquisition. Specifically, a straightforward process of quantization via simple uniform scalar quantization applied in conjunction with differential pulse code modulation of the block-based compressed-sensing measurements is proposed. Experimental results demonstrate significant improvement in rate-distortion performance as compared scalar quantization used alone in several block-based compressed-sensing reconstruction algorithms. Additionally, rate-distortion performance superior to that of alternative quantized-compressed-sensing techniques relying on optimized quantization or reconstruction is observed.

Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial or truncated Radon data problems. As a result, using a curvelet representation to invert radon data allows the chance of higher quality images to be produced. This paper examines this method of reconstruction for computed tomography (CT). A brief history of CT, an introduction to the theory behind the method, and implementation details will be provided.

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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24931号 / 情博第842号 / 新制||情||141(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 神谷 之康, 教授 熊田 孝恒, 教授 西田 眞也 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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Traditional Magnetic Resonance Imaging (MRI) reconstruction methods, which may be highly time-consuming and sensitive to noise, heavily depend on solving nonlinear optimization problems. By contrast, deep learning (DL)-based reconstruction methods do not need any explicit analytical data model and are robust to noise due to its large data-based training, which both make DL a versatile tool for fast and high-fidelity MR image reconstruction. While DL can be performed completely independently of traditional methods, it can, in fact, benefit from incorporating these established methods to achieve better results. To test this hypothesis, we proposed a hybrid DL-based MR image reconstruction method, which combines two state-of-the-art deep learning networks, U-Net and Generative Adversarial Network with Cycle loss (CycleGAN), with a traditional data reconstruction method: Projection Onto Convex Sets (POCS). Experiments were then performed to evaluate the method by comparing it to several existing state-of-the-art methods. Our results demonstrate that the proposed method outperformed the current state-of-the-art in terms of higher peak signal-to-noise ratio (PSNR) and higher Structural Similarity Index (SSIM). / Electrical and Computer Engineering

Computed Tomography (CT) finds applications across domains like medical diagnosis, security screening, and scientific research. In medical imaging, CT allows physicians to diagnose injuries and disease more quickly and accurately than other imaging techniques. However, CT is one of the most significant contributors of radiation dose to the general population and the required radiation dose for scanning could lead to cancer. On the other hand, a shallow radiation dose could sacrifice image quality causing misdiagnosis. To reduce the radiation dose, sparse-view CT, which includes capturing a smaller number of projections, becomes a promising alternative. However, the image reconstructed from linearly interpolated views possesses severe artifacts. Recently, Deep Learning-based methods are increasingly being used to interpret the missing data by learning the nature of the image formation process. The current methods are promising but operate mostly in the image domain presumably due to lack of projection data. Another limitation is the use of simulated data with less sparsity (up to 75%). This research aims to interpolate the missing sparse-view CT in the sinogram domain using deep learning. To this end, a residual U-Net architecture has been trained with patch-wise projection data to minimize Euclidean distance between the ground truth and the interpolated sinogram. The model can generate highly sparse missing projection data. The results show improvement in SSIM and RMSE by 14% and 52% respectively with respect to the linear interpolation-based methods. Thus, experimental sparse-view CT data with 90% sparsity has been successfully interpolated while improving CT image quality. / Master of Science / Computed Tomography is a commonly used imaging technique due to the remarkable ability to visualize internal organs, bones, soft tissues, and blood vessels. It involves exposing the subject to X-ray radiation, which could lead to cancer. On the other hand, the radiation dose is critical for the image quality and subsequent diagnosis. Thus, image reconstruction using only a small number of projection data is an open research problem. Deep learning techniques have already revolutionized various Computer Vision applications. Here, we have used a method which fills missing highly sparse CT data. The results show that the deep learning-based method outperforms standard linear interpolation-based methods while improving the image quality.

Fluorescence tomography (FT) is an emerging non-invasive in vivo molecular imaging modality that aims at quantification and three-dimensional (3D) localization of fluorescent tagged inclusions, such as cancer lesions and drug molecules, buried deep in human and animal subjects. Depth-resolved 3D reconstruction of fluorescent inclusions distributed over the volume of optically turbid biological tissue using the diffuse fluorescent photons detected on the skin poses a highly ill-conditioned problem, as depth information must be extracted from boundary data. Due to this ill-posed nature of FT reconstructions, noise and errors in the data can severely impair the accuracy of the 3D reconstructions. Consequently, improvements in the signal-to-noise ratio (SNR) of the data significantly enhance the quality of the FT reconstructions. Furthermore, enhancing the SNR of the FT data can greatly contribute to the speed of FT scans. The pivotal factor in the SNR of the FT data is the power of the radiation illuminating the subject and exciting the administered fluorescent agents. In existing single-point illumination FT systems, the illumination power level is limited by the skin maximum radiation exposure levels. In this research, a multiplexed architecture governed by the Hadamard transform was conceptualized, developed, and experimentally implemented for orders-of-magnitude enhancement of the SNR and the robustness of FT reconstructions. The multiplexed FT system allows for Hadamard-coded multi-point illumination of the subject while maintaining the maximal information content of the FT data. The significant improvements offered by the multiplexed FT system were validated by numerical and experimental studies carried out using a custom-built multiplexed FT system developed exclusively in this work. The studies indicate that Hadamard multiplexing offers significantly enhanced robustness in reconstructing deep fluorescent inclusions from low-SNR FT data.

[EN] Model-based computed tomography (CT) image reconstruction is dominated by iterative algorithms. Although long reconstruction times remain as a barrier in practical applications, techniques to speed up its convergence are object of investigation, obtaining impressive results. In this thesis, a direct algorithm is proposed for model-based image reconstruction. The model-based approximation relies on the construction of a model matrix that poses a linear system which solution is the reconstructed image. The proposed algorithm consists in the QR decomposition of this matrix and the resolution of the system by a backward substitution process. The cost of this image reconstruction technique is a matrix vector multiplication and a backward substitution process, since the model construction and the QR decomposition are performed only once, because of each image reconstruction corresponds to the resolution of the same CT system for a different right hand side. Several problems regarding the implementation of this algorithm arise, such as the exact calculation of a volume intersection, definition of fill-in reduction strategies optimized for CT model matrices, or CT symmetry exploit to reduce the size of the system. These problems have been detailed and solutions to overcome them have been proposed, and as a result, a proof of concept implementation has been obtained. Reconstructed images have been analyzed and compared against the filtered backprojection (FBP) and maximum likelihood expectation maximization (MLEM) reconstruction algorithms, and results show several benefits of the proposed algorithm. Although high resolutions could not have been achieved yet, obtained results also demonstrate the prospective of this algorithm, as great performance and scalability improvements would be achieved with the success in the development of better fill-in strategies or additional symmetries in CT geometry. / [ES] En la reconstrucción de imagen de tomografía axial computerizada (TAC), en su modalidad model-based, prevalecen los algoritmos iterativos. Aunque los altos tiempos de reconstrucción aún son una barrera para aplicaciones prácticas, diferentes técnicas para la aceleración de su convergencia están siendo objeto de investigación, obteniendo resultados impresionantes. En esta tesis, se propone un algoritmo directo para la reconstrucción de imagen model-based. La aproximación model-based se basa en la construcción de una matriz modelo que plantea un sistema lineal cuya solución es la imagen reconstruida. El algoritmo propuesto consiste en la descomposición QR de esta matriz y la resolución del sistema por un proceso de sustitución regresiva. El coste de esta técnica de reconstrucción de imagen es un producto matriz vector y una sustitución regresiva, ya que la construcción del modelo y la descomposición QR se realizan una sola vez, debido a que cada reconstrucción de imagen supone la resolución del mismo sistema TAC para un término independiente diferente. Durante la implementación de este algoritmo aparecen varios problemas, tales como el cálculo exacto del volumen de intersección, la definición de estrategias de reducción del relleno optimizadas para matrices de modelo de TAC, o el aprovechamiento de simetrías del TAC que reduzcan el tama\~no del sistema. Estos problemas han sido detallados y se han propuesto soluciones para superarlos, y como resultado, se ha obtenido una implementación de prueba de concepto. Las imágenes reconstruidas han sido analizadas y comparadas frente a los algoritmos de reconstrucción filtered backprojection (FBP) y maximum likelihood expectation maximization (MLEM), y los resultados muestran varias ventajas del algoritmo propuesto. Aunque no se han podido obtener resoluciones altas aún, los resultados obtenidos también demuestran el futuro de este algoritmo, ya que se podrían obtener mejoras importantes en el rendimiento y la escalabilidad con el éxito en el desarrollo de mejores estrategias de reducción de relleno o simetrías en la geometría TAC. / [CA] En la reconstrucció de imatge tomografia axial computerizada (TAC) en la seua modalitat model-based prevaleixen els algorismes iteratius. Tot i que els alts temps de reconstrucció encara són un obstacle per a aplicacions pràctiques, diferents tècniques per a l'acceleració de la seua convergència estàn siguent objecte de investigació, obtenint resultats impressionants. En aquesta tesi, es proposa un algorisme direct per a la recconstrucció de image model-based. L'aproximació model-based es basa en la construcció d'una matriu model que planteja un sistema lineal quina sol·lució es la imatge reconstruida. L'algorisme propost consisteix en la descomposició QR d'aquesta matriu i la resolució del sistema per un procés de substitució regresiva. El cost d'aquesta tècnica de reconstrucció de imatge es un producte matriu vector i una substitució regresiva, ja que la construcció del model i la descomposició QR es realitzen una sola vegada, degut a que cada reconstrucció de imatge suposa la resolució del mateix sistema TAC per a un tèrme independent diferent. Durant la implementació d'aquest algorisme sorgixen diferents problemes, tals com el càlcul exacte del volum de intersecció, la definició d'estratègies de reducció de farcit optimitzades per a matrius de model de TAC, o el aprofitament de simetries del TAC que redueixquen el tamany del sistema. Aquestos problemes han sigut detallats y s'han proposat solucions per a superar-los, i com a resultat, s'ha obtingut una implementació de prova de concepte. Les imatges reconstruides han sigut analitzades i comparades front als algorismes de reconstrucció filtered backprojection (FBP) i maximum likelihood expectation maximization (MLEM), i els resultats mostren varies ventajes del algorisme propost. Encara que no s'han pogut obtindre resolucions altes ara per ara, els resultats obtinguts també demostren el futur d'aquest algorisme, ja que es prodrien obtindre millores importants en el rendiment i la escalabilitat amb l'éxit en el desemvolupament de millors estratègies de reducció de farcit o simetries en la geometria TAC. / Iborra Carreres, A. (2015). Development of a New 3D Reconstruction Algorithm for Computed Tomography (CT) [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59421