Fourier-Based Forward and Back-Projectors in Iterative Fan-Beam Tomographic Image Reconstruction

Fourier-based forward and back-projection methods can reduce computation in iterative tomographic image reconstruction. Recently, an optimized nonuniform fast Fourier transform (NUFFT) approach was shown to yield accurate parallel-beam projections. In this paper, we extend the NUFFT approach to describe an O(N2 log N) projector/backprojector pair for fan-beam transmission tomography. Simulations and experiments with real CT data show that fan-beam Fourier-based forward and back-projection methods can reduce computation for iterative reconstruction while still providing accuracy comparable to their O(N3) space-based counterparts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86013/1/Fessler45.pd

Fourier-Based forward and back-Projectors in Iterative Fan-Beam Tomographic Image Reconstruction

Fourier-based forward and back-projection methods have the potential to reduce computation demands in iterative tomographic image reconstruction. Interpolation errors are a limitation of conventional Fourier-based projectors. Recently, the min-max optimized Kaiser-Bessel interpolation within the nonuniform fast Fourier transform (NUFFT) approach has been applied in parallel-beam image reconstruction, whose results show lower approximation errors than conventional interpolation methods. However, the extension of min-max NUFFT approach to fan-beam data has not been investigated. We have extended the min-max NUFFT framework to the fan-beam tomography case, using the relationship between the fan-beam projections and corresponding projections in parallel-beam geometry. Our studies show that the fan-beam Fourier-based forward and back-projection methods can significantly reduce the computation time while still providing comparable accuracy as their space-based counterparts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86014/1/Fessler198.pd

Reconstruction algorithms for multispectral diffraction imaging

Thesis (Ph.D.)--Boston UniversityIn conventional Computed Tomography (CT) systems, a single X-ray source spectrum is used to radiate an object and the total transmitted intensity is measured to construct the spatial linear attenuation coefficient (LAC) distribution. Such scalar information is adequate for visualization of interior physical structures, but additional dimensions would be useful to characterize the nature of the structures. By imaging using broadband radiation and collecting energy-sensitive measurement information, one can generate images of additional energy-dependent properties that can be used to characterize the nature of specific areas in the object of interest. In this thesis, we explore novel imaging modalities that use broadband sources and energy-sensitive detection to generate images of energy-dependent properties of a region, with the objective of providing high quality information for material component identification. We explore two classes of imaging problems: 1) excitation using broad spectrum sub-millimeter radiation in the Terahertz regime and measure- ment of the diffracted Terahertz (THz) field to construct the spatial distribution of complex refractive index at multiple frequencies; 2) excitation using broad spectrum X-ray sources and measurement of coherent scatter radiation to image the spatial distribution of coherent-scatter form factors. For these modalities, we extend approaches developed for multimodal imaging and propose new reconstruction algorithms that impose regularization structure such as common object boundaries across reconstructed regions at different frequencies. We also explore reconstruction techniques that incorporate prior knowledge in the form of spectral parametrization, sparse representations over redundant dictionaries and explore the advantage and disadvantages of these techniques in terms of image quality and potential for accurate material characterization. We use the proposed reconstruction techniques to explore alternative architectures with reduced scanning time and increased signal-to-noise ratio, including THz diffraction tomography, limited angle X-ray diffraction tomography and the use of coded aperture masks. Numerical experiments and Monte Carlo simulations were conducted to compare performances of the developed methods, and validate the studied architectures as viable options for imaging of energy-dependent properties

Streaming Architectures for Medical Image Reconstruction

Non-invasive imaging modalities have recently seen increased use in clinical diagnostic procedures. Unfortunately, emerging computational imaging techniques, such as those found in 3D ultrasound and iterative magnetic resonance imaging (MRI), are severely limited by the high computational requirements and poor algorithmic efficiency in current arallel hardware---often leading to significant delays before a doctor or technician can review the image, which can negatively impact patients in need of fast, highly accurate diagnosis. To make matters worse, the high raw data bandwidth found in 3D ultrasound requires on-chip volume reconstruction with a tight power dissipation budget---dissipation of more than 5~W may burn the skin of the patient. The tight power constraints and high volume rates required by emerging applications require orders of magnitude improvement over state-of-the-art systems in terms of both reconstruction time and energy efficiency. The goal of the research outlined in this dissertation is to reduce the time and energy required to perform medical image reconstruction through software/hardware co-design. By analyzing algorithms with a hardware-centric focus, we develop novel algorithmic improvements which simultaneously reduce computational requirements and map more efficiently to traditional hardware architectures. We then design and implement hardware accelerators which push the new algorithms to their full potential. In the first part of this dissertation, we characterize the performance bottlenecks of high-volume-rate 3D ultrasound imaging. By analyzing the 3D plane-wave ultrasound algorithm, we reduce computational and storage requirements in Delay Compression. Delay Compression recognizes additional symmetry in the planar transmission scheme found in 2D, 3D, and 3D-Separable plane-wave ultrasound implementations, enabling on-chip storage of the reconstruction constants for the first time and eliminating the ost power-intensive component of the reconstruction process. We then design and implement Tetris, a streaming hardware accelerator for 3D-Separable plane-wave ultrasound. Tetris is enabled by the Tetris Reserveration Station, a novel 2D register file that buffers incomplete voxels and eliminates the need for a traditional load-and-store memory interface. Utilizing a fully pipelined architecture, Tetris reconstructs volumes at physics-limited rates (i.e., limited by the physical propagation speed of sound through tissue). Next, we review a core component of several computational imaging modalities, the Non-uniform Fast Fourier Transform (NuFFT), focusing on its use in MRI reconstruction. We find that the non-uniform interpolation step therein requires over 99% of the reconstruction time due to poor spatial and temporal memory locality. While prior work has made great strides in improving the performance of the NuFFT, the most common algorithmic optimization severely limits the available parallelism, causing it to map poorly to the massively parallel processing available in modern GPUs and FPGAs. To this end, we create Slice-and-Dice, a processing model which enables efficient mapping of the NuFFT's most computationally-intensive component onto traditional parallel architectures. We then demonstrate the full acceleration potential of Slice-and-Dice with Jigsaw, a custom hardware accelerator which performs the non-uniform interpolations found in the NuFFT in time approximately linear in the number of non-uniform samples, rrespective of sampling pattern, uniform grid size, or interpolation kernel width. The algorithms and architectures herein enable faster, more efficient medical image reconstruction, without sacrificing image quality. By decreasing the time and energy required for image reconstruction, our work opens the door for future exploration into higher-resolution imaging and emerging, computationally complex reconstruction algorithms which improve the speed and quality of patient diagnosis.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/167986/1/westbl_1.pd

Advanced H-1 Lung Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is one of the widely used medical imaging modality, since it can provide both structural and functional assessment in a single imaging session. However, two major challenges should be considered by using MRI for lung imaging. The first challenge is the intrinsic low SNR of H-1 lung MRI due to the low proton density as well as the fast decay of the lung parenchyma signal. And the second challenge is subject motion. To achieve high resolution structural image, MRI requires a long scan time, usually a few minutes or even longer, which make MRI sensitive to subject motion. To address the first challenge, ultra-short echo time (UTE) MRI sequence is used to capture the lung parenchyma signal before decay. As for subject motion, two major strategies are widely used. One strategy is fast breath-holding scan, the subjects are asked to hold their breaths for a short duration, and the fast 3D MR sequence would be used to acquire data within that duration. This dissertation proposes a new acquisition scheme based on the standard UTE sequence, which largely increases the encoding efficiency and improves the breath-holding scan images. The other is free breathing scan with motion correction. The subjects are allowed to breathe during the MR acquisition. After the acquisition, the motion corrupted data would go through the motion correction step to reconstruct the motion free images. In this dissertation, two novel motion corrected reconstruction strategies are proposed to incorporate the motion modeling and compensation into the reconstruction to get high SNR motion corrected 3D and 4D images. When translating the developed techniques to the clinical studies, specifically for pediatric and neonatal studies, more practical problems need to be considered, such as smaller but finer anatomy to image, the different respiratory patterns of the young subjects etc. This dissertation proposes a 5-minute free breathing UTE MRI strategy to achieve a 3D high resolution motion free lung image for pediatric and neonatal studies

Accelerated respiratory-resolved 4D-MRI with separable spatio-temporal neural networks

Background: Respiratory-resolved four-dimensional magnetic resonance imaging (4D-MRI) provides essential motion information for accurate radiation treatments of mobile tumors. However, obtaining high-quality 4D-MRI suffers from long acquisition and reconstruction times. Purpose: To develop a deep learning architecture to quickly acquire and reconstruct high-quality 4D-MRI, enabling accurate motion quantification for MRI-guided radiotherapy. Methods: A small convolutional neural network called MODEST is proposed to reconstruct 4D-MRI by performing a spatial and temporal decomposition, omitting the need for 4D convolutions to use all the spatio-temporal information present in 4D-MRI. This network is trained on undersampled 4D-MRI after respiratory binning to reconstruct high-quality 4D-MRI obtained by compressed sensing reconstruction. The network is trained, validated, and tested on 4D-MRI of 28 lung cancer patients acquired with a T1-weighted golden-angle radial stack-of-stars sequence. The 4D-MRI of 18, 5, and 5 patients were used for training, validation, and testing. Network performances are evaluated on image quality measured by the structural similarity index (SSIM) and motion consistency by comparing the position of the lung-liver interface on undersampled 4D-MRI before and after respiratory binning. The network is compared to conventional architectures such as a U-Net, which has 30 times more trainable parameters. Results: MODEST can reconstruct high-quality 4D-MRI with higher image quality than a U-Net, despite a thirty-fold reduction in trainable parameters. High-quality 4D-MRI can be obtained using MODEST in approximately 2.5 minutes, including acquisition, processing, and reconstruction. Conclusion: High-quality accelerated 4D-MRI can be obtained using MODEST, which is particularly interesting for MRI-guided radiotherapy.Comment: Code available at https://gitlab.com/computational-imaging-lab/modes

Uma nova abordagem para o uso de métodos diretos na reconstrução de imagens médicas com compressive sensing

Dissertação (mestrado) — Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2022.A partir das tecnologias de imageamento médico, profissionais de saúde conseguem informações relevantes sobre o estado de um paciente para o planejamento e acompanhamento de seu tratamento. A Tomografia Computadorizada por raios-x (CT) e a Ressonância Magnética (MR) são duas das tecnologias mais bem consolidadas no meio. Estas técnicas permitem a obtenção de imagens anatômicas de planos específicos ou volumes. Apesar de a CT e a MR explorarem princípios físicos diferentes, ambas coletam medidas que podem ser modeladas como coeficientes da Transformada de Fourier da imagem a ser reconstruída. O processo de reconstrução refere-se a etapa de calcular a imagem desejada a partir das medidas adquiridas pelos equipamentos médicos. A aquisição geralmente requer que o paciente permaneça em uma mesma posição por longos períodos e, no caso da CT, há a emissão de radiação ionizante. Assim, é de interesse que tais procedimentos ocorram da forma mais segura e rápida possível. Uma maneira de abordar este problema é o desenvolvimento de algoritmos de reconstrução que consigam gerar imagens úteis para a atividade clínica usando uma quantidade reduzida de medidas. Conceitos de Compressive Sensing (CS) vem sendo adotados na elaboração de novos algoritmos para reconstrução de imagens médicas em vista de uma aquisição mais eficiente. Esta área de conhecimento estuda a reconstrução de sinais a partir de medidas incompletas por meio da resolução de sistemas lineares subdeterminados. O sinal de interesse é a solução cuja maior parte dos coeficientes é nula. Ou seja, considera-se que o sinal reconstruído possui uma representação esparsa em algum domínio conhecido. A minimização de `p (0 < p ≤ 1) é uma estratégia frequentemente explorada por algoritmos de CS. Adotar métricas `p com menores valores de p, apesar de recair em problemas não-convexos, pode possibilitar uma redução ainda maior de medidas. Imagens são sinais de grande dimensão. Por esta razão, técnicas de reconstrução que se baseiam em CS recorrem a métodos indiretos para a realização de operações matriciais, já que o armazenamento das matrizes que modelam o problema é inviável durante a execução dos algoritmos. A estabilidade e a convergência dos métodos indiretos são afetadas pela redução do valor de p de modo que esta estratégia não pode ser bem explorada ao executar as operações matriciais indiretamente. Neste contexto, a presente pesquisa desenvolve a Estrutura de Reconstrução Direta (DRS) para formação de imagens médicas por meio da composição de sinais de menor dimensão, que são obtidos através de minimização de `p. Inicialmente, apresentamos o formalismo matemático para implementações genéricas dessa estrutura, em que não se assume nenhuma operação específica para a composição. Em um segundo momento, derivamos o modelo matemático e o problema de minimização para uma formulação que compõe a imagem a partir de sinais unidimensionais, que contém a informação de uma linha de medidas no plano de frequências. Implementamos esta formulação específica do DRS usando o IRLS (Iteratively Reweighted Least Squares) como algoritmo de minimização e a pré-filtragem para a representação esparsa. Realizamos quatro experimentos numéricos com o objetivo de investigar o comportamento dos algoritmos de CS ao reduzirmos o valor de p e avaliar a performance do DRS em comparação às técnicas que usam método indireto. Em nossos testes usamos tanto sinais artificiais como dados de imagens reais. Os resultados apontam que o DRS reconstrói satisfatoriamente as imagens médicas em condições favoráveis de esparsidade. A pré-filtragem não obteve a mesma eficiência em esparsificar os sinais reconstruídos pelo DRS em comparação ao que é verificado no caso dos algoritmos que usam método indireto.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).With the support of medical imaging technologies, healthcare workers are provided with relevant information about a patient’s condition when planning and following up on treatment. X-ray Computed Tomography (CT) and Magnetic Resonance (MR) are two of the most consolidated technologies in the field. These techniques yield anatomical images of specific planes or volumes. Although CT and MR exploit different physical principles, both collect measurements that can be modeled as the Fourier Transform coefficients of the image to be reconstructed. The reconstruction procedure refers to the stage of computing the desired image from the measurements acquired by the medical equipment. The acquisition usually requires the patient to stay in the same position for long periods, and, in the case of CT, there is the emission of ionizing radiation. Thus, such procedures should take place as safely and quickly as possible. A possible approach to address this issue is the development of reconstruction algorithms that can generate meaningful images for clinical practice from a reduced amount of measurements. Concepts of Compressive Sensing (CS) have been adopted in the devising of new algorithms for medical imaging to achieve a more efficient acquisition. This area of knowledge studies the reconstruction of signals from incomplete measurements by solving underdetermined linear systems. The signal of interest is the solution whose most of the coefficients are null. That is, the reconstructed signal is assumed to have a sparse representation in a known domain. Minimizing `p (0 < p ≤ 1) is a strategy often exploited by CS algorithms. Adopting `p metrics with smaller values of p, even leading to non-convex problems, opens up the possibility of further reductions in the number of measurements. Images are large signals. For this reason, CS-based reconstruction techniques rely on indirect methods to perform matrix operations because the storage of the matrices that model the problem is impractical during the execution of the algorithms. The stability and convergence of indirect methods are affected by reducing the value of p so that this strategy cannot be well exploited when performing matrix operations indirectly. In this background, the present research devises the Direct Reconstruction Structure (DRS) for medical image formation through the composition of lower-dimensional signals, which are obtained through `p minimization. First, we present the mathematical formalism for generic implementations of this structure, which makes no assumptions about the operation for composition. Following, we derive the mathematical model and the minimization problem for a formulation that composes the image from onedimensional signals, which contain the information of a row of measurements in the frequency plane. We implemented that specific DRS formulation using the Iteratively Reweighted Least Squares (IRLS) as the minimization algorithm and prefiltering for sparse representation. We conducted four numerical experiments to investigate the behavior of the CS algorithms when reducing the value of p and evaluate the performance of DRS compared to techniques using an indirect method. In our tests, we used both artificial signals and actual image data. The results suggest that DRS can satisfactorily reconstruct medical images in good sparsity conditions. Prefiltering did not achieve the same effect in sparsifying the signals reconstructed by DRS compared to the case of algorithms using the indirect method