Image reconstruction in SNR units: a general method for SNR measurement

Abstract

The method for phased array image reconstruction of uniform noise images may be used in conjunction with proper image scaling as a means of reconstructing images directly in SNR units. This facilitates accurate and precise SNR measurement on a per pixel basis. This method is applicable to root-sum-of-squares magnitude combining, B(1)-weighted combining, and parallel imaging such as SENSE. A procedure for image reconstruction and scaling is presented, and the method for SNR measurement is validated with phantom data. Alternative methods that rely on noise only regions are not appropriate for parallel imaging where the noise level is highly variable across the field-of-view. The purpose of this article is to provide a nuts and bolts procedure for calculating scale factors used for reconstructing images directly in SNR units. The procedure includes scaling for noise equivalent bandwidth of digital receivers, FFTs and associated window functions (raw data filters), and array combining.

Figures

FIG. 1

(a) Image reconstruction steps. (b) Individual signal processing step with unity gain for noise SD.

FIG. 2

Step-by-Step procedure.

FIG. 3

Procedure for SNR scaled image reconstruction (p is complex vector of multi-coil images, b is complex vector of coil sensitivities, u is complex vector of SENSE unmixing coefficients, Rn is noise correlation matrix, and Bn is noise equivalent bandwidth).

FIG. 4

Average noise spectrum.

FIG. 5

Low SNR magnitude correction curves (Nc = number of channels combined).

FIG. 6

Root-Sum-of-Squares (RSS) combined magnitude image reconstruction example: (a) average SNR scaled image (256 trials averaged), (b) SD of SNR scaled images (256 trials), (c) direct SNR estimate computed as ratio of (a) and (b) (note that (a) and (c) are displayed with same window-level and are in close agreement).

FIG. 7

SENSE combined image reconstruction example: (a) average SNR scaled image (256 trials averaged), (b) SD of SNR scaled images (256 trials), (c) direct SNR estimate computed as ratio of (a) and (b) (note that (a) and (c) are displayed with same window-level and are in close agreement).

FIG. 8

SENSE combined image reconstruction example: (a) average SNR scaled image without including g-factor term (256 trials averaged), (b) SD of images (256 trials) in (a) is direct estimate of SENSE g-factor, (c) estimate of SENSE g-factor computed from complex coil sensitivities (note that (b) and (c) are displayed with same window-level, 1 < g < 1.4).

FIG. 9

Short-Axis cardiac imaging example of SNR scaled uniform noise reconstructions using full k-space RSS combined magnitude and SENSE acceleration rates 2, 3, and 4 (left to right) with phase encoding direction AP (top row) and LR (bottom row). Note that the bottom row images have approximately 2SNR due to the double acquisition time required for LR encoding to achieve approximately the same temporal and spatial resolution.

FIG.10

SENSE g-factor computed from raw complex coil sensitivities for rates 2, 3, and 4 (left to right) with phase encoding direction AP (top row) and LR (bottom row) for same cases and FOV as in Fig. 9, with the ellipse corresponding to the heart region.

FIG. 11

Magnitude of difference between consecutive image frames illustrates contamination of background noise estimate due to motion using this method: (a) end-systolic phase with large residual due to motion, (b) end-diastolic phase with small residual (0 < Δl < 16σ).

FIG. 12

Monte-Carlo simulation results for magnitude noise correction for single-pixel and 3 × 3 pixel average for Nc = 1 and 8 coils. The RMSE provided combined measure of accuracy and precision.