Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs

Fessler, Jeffrey A.; Rogers, W.L.

doi:10.1109/83.535846

Cited by 482 publications

(360 citation statements)

References 33 publications

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“…We believe this is caused by the smoothing prior, which smooths more in planes further from the detector, because the likelihood provides less information there. A possible solution which we will investigate, is to vary the prior strength as a function of the position, aiming at a more uniform balance between prior and likelihood [38].…”

Section: Discussionmentioning

confidence: 99%

Patchwork reconstruction with resolution modeling for digital breast tomosynthesis

2013

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Purpose: Digital breast tomosynthesis is a relatively new diagnostic x-ray modality that allows high resolution breast imaging while suppressing interference from overlapping anatomical structures. However, proper visualization of micro-calcifications remains a challenge. For the subset of systems we consider, the main cause of deterioration is movement of the x-ray source during exposures. We propose a modified grouped coordinate ascent algorithm that includes a specific acquisition model to compensate for this deterioration.Methods: We create a resolution model based on the movement of the x-ray source during image acquisition and combine this with a grouped coordinate ascent algorithm. Choosing planes parallel to the detector surface as the groups enables efficient implementation of the position dependent resolution model. In the current implementation, the resolution model is approximated by a Gaussian smoothing kernel.The effect of the resolution model on the iterative reconstruction is evaluated by measuring contrast to noise ratio (CNR) of spherical micro-calcifications in a homogeneous background. After this, our new reconstruction method is compared to the optimized filtered backprojection method for the considered system, by performing two observer studies: the first study simulates clusters of spherical micro-calcifications in a power law background for a free search task; the second study simulates smooth or irregular micro-calcifications in the same type of backgrounds for a classification task.Results: Including the resolution model in the iterative reconstruction methods increases the CNR of micro-calcifications. The first observer study shows a significant improvement in detection of micro-calcifications (p = 0.029) while the second study shows that performance on a classification task remains the same (p = 0.935) compared to the filtered backprojection method.Conclusions: Our method shows higher CNR and improved visualization of micro-calcifications in an observer experiment on synthetic data. Further study of the negative results of the classification task showed performance variations throughout the volume linked to the changing noise structure introduced by the combination of the resolution model and the smoothing prior.

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Section: Discussionmentioning

confidence: 99%

Patchwork reconstruction with resolution modeling for digital breast tomosynthesis

2013

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“…Using the results in [12] and [11], the local impulse response of MAP reconstruction can be approximated by…”

Section: Lesion Detectability In Map Reconstructionmentioning

confidence: 99%

“…An alternative approach was proposed by Fessler and Rogers [11,12], who analyzed the mean, variance, and spatial resolution at a fixed point of the objective function. The resolution and noise properties are computed at the fixed point using partial derivatives and truncated Taylor series approximations.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Evaluation of the Detectability of Random Lesions in Bayesian Emission Reconstruction

2003

Lecture Notes in Computer Science

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Abstract. Detecting cancerous lesion is an important task in positron emission tomography (PET). Bayesian methods based on the maximum a posteriori principle (also called penalized maximum likelihood methods) have been developed to deal with the low signal to noise ratio in the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the prior parameters in Bayesian reconstruction control the resolution and noise trade-off and hence affect detectability of lesions in reconstructed images. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Most research has been based on Monte Carlo simulations, which are very time consuming. Building on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers, here we develop a theoretical approach for fast computation of lesion detectability in Bayesian reconstruction. The results can be used to choose the optimum hyperparameter for the maximum lesion detectability. New in this work is the use of theoretical expressions that explicitly model the statistical variation of the lesion and background without assuming that the object variation is (locally) stationary. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predications and the Monte Carlo results.

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“…The idea is based on the observation that F and F + βR are diagonally dominant and are smoothly varying along the diagonal. 6,7 This allows us to use the locally stationary approximation 10…”

Section: Fast Computationmentioning

confidence: 99%

“…Recently, progress has been made in understanding the nonlinear properties of statistical reconstruction methods. [5][6][7][8][9][10][11] Barrett et al 5 derived approximate formulae for the mean and covariance of the maximum likelihood (ML) expectation maximization (EM) reconstruction as a function of the iteration number. The same approach was extended to maximum a posteriori (MAP) EM algorithms by Wang and Gindi 8 and most recently to block iterative algorithms by Soares et al 12 This iteration-based approach is attractive for methods that are terminated before convergence, as is common practice for the EM algorithm and its ordered-subsets variants.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Bayesian emission tomographic reconstruction for region-of-interest quantitation

2003

SPIE Proceedings

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Region of interest (ROI) quantitation is an important task in emission tomography (e.g., positron emission tomography and single photon emission computed tomography). It is essential for exploring clinical factors such as tumor activity, growth rate, and the efficacy of therapeutic interventions. Bayesian methods based on the maximum a posteriori principle (or called penalized maximum likelihood methods) have been developed for emission image reconstructions to deal with the low signal to noise ratio of the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the smoothing parameter of the image prior in Bayesian reconstruction controls the resolution and noise trade-off and hence affects ROI quantitation. In this paper we present an approach for choosing the optimum smoothing parameter in Bayesian reconstruction for ROI quantitation. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Building on the recent progress on deriving the approximate expressions for the local impulse response function and the covariance matrix, we derived simplified theoretical expressions for the bias, the variance, and the ensemble mean squared error (EMSE) of the ROI quantitation. One problem in evaluating ROI quantitation is that the truth is often required for calculating the bias. This is overcome by using ensemble distribution of the activity inside the ROI and computing the average EMSE. The resulting expressions allow fast evaluation of the image quality for different smoothing parameters. The optimum smoothing parameter of the image prior can then be selected to minimize the EMSE.

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Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs

Cited by 482 publications

References 33 publications

Patchwork reconstruction with resolution modeling for digital breast tomosynthesis

Patchwork reconstruction with resolution modeling for digital breast tomosynthesis

Theoretical Evaluation of the Detectability of Random Lesions in Bayesian Emission Reconstruction

Optimization of Bayesian emission tomographic reconstruction for region-of-interest quantitation

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