RESUMO
This paper describes a new method for estimating the 3D, non-rigid object motion in a time sequence of images. The method is a generalization of a standard optical flow algorithm that is incorporated into a successive quadratic approximation framework. The method was evaluated for gated cardiac emission tomography using images obtained from a mathematical, 4D phantom and a physical, dynamic phantom. The results showed that the proposed method offers improved motion estimation accuracy relative to the standard optical flow method. Convergence of the proposed algorithm was evidenced with a monotonically decreasing objective function value with iteration. Practical application of the motion estimation method in cardiac emission tomography includes quantitative myocardial motion estimation and 4D, motion-compensated image reconstruction.
Assuntos
Algoritmos , Coração/fisiologia , Imageamento Tridimensional , Movimento/fisiologia , Imagens de Fantasmas , Simulação por Computador , Humanos , Tomografia Óptica/métodosRESUMO
In this paper, we propose and test a new iterative algorithm to simultaneously estimate the nonrigid motion vector fields and the emission images for a complete cardiac cycle in gated cardiac emission tomography. We model the myocardium as an elastic material whose motion does not generate large amounts of strain. As a result, our method is based on minimizing an objective function consisting of the negative logarithm of a maximum likelihood image reconstruction term, the standard biomechanical model of strain energy, and an image matching term that ensures a measure of agreement of intensities between frames. Simulations are obtained using data for the four-dimensional (4-D) NCAT phantom. The data models realistic noise levels in a typical gated myocardial perfusion SPECT study. We show that our simultaneous algorithm produces images with improved spatial resolution characteristics and noise properties compared with those obtained from postsmoothed 4-D maximum likelihood methods. The simulations also demonstrate improved motion estimates over motion estimation using independently reconstructed images.
Assuntos
Algoritmos , Imagem do Acúmulo Cardíaco de Comporta/métodos , Coração/diagnóstico por imagem , Aumento da Imagem/métodos , Interpretação de Imagem Assistida por Computador/métodos , Imageamento Tridimensional/métodos , Tomografia Computadorizada de Emissão/métodos , Imagem do Acúmulo Cardíaco de Comporta/instrumentação , Armazenamento e Recuperação da Informação/métodos , Movimento (Física) , Imagens de Fantasmas , Reprodutibilidade dos Testes , Sensibilidade e Especificidade , Tomografia Computadorizada de Emissão/instrumentaçãoRESUMO
We present penalized weighted least-squares (PWLS) and penalized maximum-likelihood (PML) methods for reconstructing transmission images from positron emission tomography transmission data. First, we view the problem of minimizing the weighted least-squares (WLS) and maximum likelihood objective functions as a sequence of nonnegative least-squares minimization problems. This viewpoint follows from using certain quadratic functions as surrogate functions for the WLS and maximum likelihood objective functions. Second, we construct surrogate functions for a class of penalty functions that yield closed form expressions for the iterates of the PWLS and PML algorithms. Due to the slow convergence of the PWLS and PML algorithms, accelerated versions of them are developed that are theoretically guaranteed to monotonically decrease their respective objective functions. In experiments using real phantom data, the PML images produced the most accurate attenuation correction factors. On the other hand, the PWLS images produced images with the highest levels of contrast for low-count data.
Assuntos
Algoritmos , Aumento da Imagem/métodos , Interpretação de Imagem Assistida por Computador/métodos , Modelos Biológicos , Reconhecimento Automatizado de Padrão/métodos , Tomografia por Emissão de Pósitrons/métodos , Tórax/diagnóstico por imagem , Inteligência Artificial , Análise por Conglomerados , Simulação por Computador , Humanos , Imageamento Tridimensional/métodos , Armazenamento e Recuperação da Informação/métodos , Análise dos Mínimos Quadrados , Funções Verossimilhança , Modelos Estatísticos , Imagens de Fantasmas , Tomografia por Emissão de Pósitrons/instrumentação , Reprodutibilidade dos Testes , Sensibilidade e EspecificidadeRESUMO
We present unpenalized and penalized weighted least-squares (WLS) reconstruction methods for positron emission tomography (PET), where the weights are based on the covariance of a model error and depend on the unknown parameters. The penalty function for the latter method is chosen so that certain a priori information is incorporated. The algorithms used to minimize the WLS objective functions guarantee nonnegative estimates and, experimentally, they converged faster than the maximum likelihood expectation-maximization (ML-EM) algorithm and produced images that had significantly better resolution and contrast. Although simulations suggest that the proposed algorithms are globally convergent, a proof of convergence has not yet been found. Nevertheless, we are able to show that the unpenalized method produces estimates that decrease the objective function monotonically with increasing iterations.
