### Abstract

Signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and otTers a substantial improvement, as measured by the ensemble-mean squared error (EMSE), when compared to using voxel values from a maximum-likelihood expectationmaximization (MLEM) reconstructed ROI. The scanning-linear estimator is derived as a special case of maximum-likelihood (ML) techniques with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise, and variability in the signal's activity. The resulting estimate of the signal activity is an unbiased estimator: the average estimate equals the true value. By contrast, algorithms that operate on reconstructed data are subject to unpredictable bias arising from the null functions of the imaging system and the object. Using visual inspetion of reconstructed data to select an ROI is tantamoun to estimating a location and size of the signal. general, this procedure would less than ideal, but we remove this source of error by estimating the activity of a spherical signal whose radius and centroid are known. The signal shape and location fully specify a binary ROI template in object space. Although the scanning-linear method can be generalized to more complicated estimation tasks, we will demonstrate its use for estimating only signal amplitude. Noisy projection data are realistically emulated using measured calibration data from the multi-module multiresolution (M _{3}R) small-animal SPECT imaging system. The scanning-linear estimate of signal activity is computed for 800 image samples. The same set of images are reconstructed using the MLEM algorithm (80 iterations), and the mean as well as the maximum value within the ROI is calculated.

Original language | English (US) |
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Title of host publication | IEEE Nuclear Science Symposium Conference Record |

Pages | 5332-5334 |

Number of pages | 3 |

DOIs | |

State | Published - 2008 |

Event | 2008 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2008 - Dresden, Germany Duration: Oct 19 2008 → Oct 25 2008 |

### Other

Other | 2008 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2008 |
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Country | Germany |

City | Dresden |

Period | 10/19/08 → 10/25/08 |

### Fingerprint

### Keywords

- Assessment of image quality
- SPECT
- Terms-Estimation

### ASJC Scopus subject areas

- Radiation
- Nuclear and High Energy Physics
- Radiology Nuclear Medicine and imaging

### Cite this

*IEEE Nuclear Science Symposium Conference Record*(pp. 5332-5334). [4774436] https://doi.org/10.1109/NSSMIC.2008.4774436

**Bias in roj estimators and an unbiased solution.** / Kupinski, Meridith Kathryn; Clarkson, Eric W; Barrett, Harrison H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE Nuclear Science Symposium Conference Record.*, 4774436, pp. 5332-5334, 2008 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2008, Dresden, Germany, 10/19/08. https://doi.org/10.1109/NSSMIC.2008.4774436

}

TY - GEN

T1 - Bias in roj estimators and an unbiased solution

AU - Kupinski, Meridith Kathryn

AU - Clarkson, Eric W

AU - Barrett, Harrison H

PY - 2008

Y1 - 2008

N2 - Signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and otTers a substantial improvement, as measured by the ensemble-mean squared error (EMSE), when compared to using voxel values from a maximum-likelihood expectationmaximization (MLEM) reconstructed ROI. The scanning-linear estimator is derived as a special case of maximum-likelihood (ML) techniques with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise, and variability in the signal's activity. The resulting estimate of the signal activity is an unbiased estimator: the average estimate equals the true value. By contrast, algorithms that operate on reconstructed data are subject to unpredictable bias arising from the null functions of the imaging system and the object. Using visual inspetion of reconstructed data to select an ROI is tantamoun to estimating a location and size of the signal. general, this procedure would less than ideal, but we remove this source of error by estimating the activity of a spherical signal whose radius and centroid are known. The signal shape and location fully specify a binary ROI template in object space. Although the scanning-linear method can be generalized to more complicated estimation tasks, we will demonstrate its use for estimating only signal amplitude. Noisy projection data are realistically emulated using measured calibration data from the multi-module multiresolution (M 3R) small-animal SPECT imaging system. The scanning-linear estimate of signal activity is computed for 800 image samples. The same set of images are reconstructed using the MLEM algorithm (80 iterations), and the mean as well as the maximum value within the ROI is calculated.

AB - Signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and otTers a substantial improvement, as measured by the ensemble-mean squared error (EMSE), when compared to using voxel values from a maximum-likelihood expectationmaximization (MLEM) reconstructed ROI. The scanning-linear estimator is derived as a special case of maximum-likelihood (ML) techniques with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise, and variability in the signal's activity. The resulting estimate of the signal activity is an unbiased estimator: the average estimate equals the true value. By contrast, algorithms that operate on reconstructed data are subject to unpredictable bias arising from the null functions of the imaging system and the object. Using visual inspetion of reconstructed data to select an ROI is tantamoun to estimating a location and size of the signal. general, this procedure would less than ideal, but we remove this source of error by estimating the activity of a spherical signal whose radius and centroid are known. The signal shape and location fully specify a binary ROI template in object space. Although the scanning-linear method can be generalized to more complicated estimation tasks, we will demonstrate its use for estimating only signal amplitude. Noisy projection data are realistically emulated using measured calibration data from the multi-module multiresolution (M 3R) small-animal SPECT imaging system. The scanning-linear estimate of signal activity is computed for 800 image samples. The same set of images are reconstructed using the MLEM algorithm (80 iterations), and the mean as well as the maximum value within the ROI is calculated.

KW - Assessment of image quality

KW - SPECT

KW - Terms-Estimation

UR - http://www.scopus.com/inward/record.url?scp=67649226072&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649226072&partnerID=8YFLogxK

U2 - 10.1109/NSSMIC.2008.4774436

DO - 10.1109/NSSMIC.2008.4774436

M3 - Conference contribution

SN - 9781424427154

SP - 5332

EP - 5334

BT - IEEE Nuclear Science Symposium Conference Record

ER -