Simplified approach for measuring image noise in reconstructed nuclear medicine images using frequency domain masking.

Objectives: The assessment of image noise in reconstructed datasets can be challenging because of the non-Poisson nature of reconstructed data. Methods that attempt to measure image noise in the spatial domain are difficult because of the challenge of establish the true signal in the presence variation in tracer uptake. We describe a simple method for separating the noise component from the object component by using a zero mask of the low frequency component of the Fourier transform.

Methods: The application of Fourier transform to noisy image data typically confines object information to the lower frequencies. In contrast, the mean amplitude of the random noise component is equally distributed across all frequencies. The method described herein first applies a fast Fourier transform (FFT) to the image. We then apply a circular zeroing mask to all frequencies below a certain threshold value. The extent of this mask defined by the size of the object in the Fourier domain (limited by the intrinsic resolution of the image). An inverse FFT is applied to the masked FFT create a “noise-only” image. The “noise only” image is then re-normalized to account for the lost information of the FFT that has been zeroed out. The signal to noise ratio (SNR-FFT) is defined as the average counts in the myocardial ROI of the original image divided by the counts in the same ROI in the noise-only image. This method was tested on a uniform cardiac phantom (Data Spectrum, Durham NC). The phantom was acquired on a CardioMD (Philips Medical System, Cleveland OH) system using a 16 gate acquisition. Sixteen summed projection datasets were created from the gated data (gate 1, gate 1 + gate 2, etc). Image noise was measured in a cardiac ROI in the unfiltered projection data utilizing three different reconstruction methods filtered back projection (FBP), 2D-OSEM, and OSEM with resolution recovery (RR-OSEM). The SNR-FFT was compared to the square root of the mean counts in the myocardial ROI in the original image (SNR).

Results: Comparison of the SNR-FFT and SNR demonstrated a very high degree of correlation in the raw data and a slope of nearly unity (slope = 1.031, intercept = 0.155, r²=0.9986). For reconstructions, SNR-FFT for short acquisition times was also highly correlated with the square root of the acquisition time similar to Poisson data. Longer acquisition times converged to a value limited by the post-filter (Low pass, 5^th order, 0.4 Nyquist) and intrinsic resolution. Visual review of the residual “noise-only” images of the 2D-OSEM and RR-OSEM confirmed that high resolution features were present in the long acquisition time images.

Conclusion: SNR-FFT in projection images is highly correlated with the square root of the mean counts (similar to Poisson distributed noise). SNR-FFT in reconstructed images is also highly correlated with the square root of acquisition time at shorter acquisitions times then converged to a maximum SNR-FFT. The RR-OSEM technique converged in the shortest time. This simplified, objective measure of image noise could prove useful in comparing noise relationships of differing filtering techniques, reconstruction algorithms and Bayesian constraints. Research Support: None