Modeling human observer detection in undersampled magnetic resonance imaging MRI reconstruction with total variation and wavelet sparsity regularization

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Modeling human observer detection in undersampled magnetic

resonance imaging (MRI) reconstruction with total variation and

wavelet sparsity regularization

Alexandra G. O’Neilla, Emely L. Valdeza, Sajan Goud Lingalab, Angel R. Pinedaa,*

aManhattan College, Department of Mathematics, 4513 Manhattan College Pkwy, The Bronx, NY, USA, 10471

bUniversity of Iowa, Roy J. Carver Department of Biomedical Engineering, Iowa City, IA, USA, 52242

Abstract.

Purpose: Task-based assessment of image quality in undersampled magnetic resonance imaging (MRI) provides a

way of evaluating the impact of regularization on task performance. In this work, we evaluated the effect of total

variation (TV) and wavelet regularization on human detection of signals with a varying background and validated a

model observer in predicting human performance.

Approach: Human observer studies used two-alternative forced choice (2-AFC) trials with a small signal known ex-

actly (SKE) task but with varying backgrounds for ﬂuid-attenuated inversion recovery (FLAIR) images reconstructed

from undersampled multi-coil data. We used a 3.48 undersampling factor with TV and a wavelet sparsity constraints.

The sparse difference-of-Gaussians (S-DOG) observer with internal noise was used to model human observer detec-

tion. The internal noise for the S-DOG was chosen to match the average percent correct (PC) in 2-AFC studies for

four observers using no regularization. That S-DOG model was used to predict the percent correct of human observers

for a range of regularization parameters.

Results: We observed a trend that the human observer detection performance remained fairly constant for a broad

range of values in the regularization parameter before decreasing at large values. A similar result was found for the

normalized ensemble root mean squared error (ERMSE). Without changing the internal noise, the model observer

tracked the performance of the human observers as the regularization was increased but over-estimated the PC for

large amounts of regularization for TV and wavelet sparsity, as well as the combination of both parameters.

Conclusions: For the task we studied, the S-DOG observer was able to reasonably predict human performance with

both total variation and wavelet sparsity regularizers over a broad range of regularization parameters. We observed

a trend that task performance remained fairly constant for a range of regularization parameters before decreasing for

large amounts of regularization.

Keywords: model observers, magnetic resonance imaging, constrained reconstruction, image quality assessment.

*Angel R. Pineda, angel.pineda@manhattan.edu

1 Introduction

Task-based assessment of image quality1,2for reconstructed MRI images is critical to the develop-

ment and validation of accelerated reconstruction techniques. This approach has been extensively

used in other imaging modalities3–12 There has been research using task-based techniques in MRI

for parallel imaging13 and compressed sensing14 but most methods utilized for assessment of image

quality in MRI are typically root mean square error (RMSE) and structural similarity index (SSIM).

arXiv:2210.11965v2 [physics.med-ph] 10 Mar 2023

These are measures of pixel value differences between the original and reconstructed image.15,16

While these measures do give an indication of similarity between images, neither RMSE nor SSIM

take into account the speciﬁc task for which the image will be used. As a result, images with the

same RMSE and SSIM could produce different performance in these tasks. Observer models are

an alternative way to assess image quality by taking into account human visual principles as well

as the task for which the image will be used.17–19

Previous results related to evaluating MRI reconstruction of undersampled images using an ap-

proximation to the ideal linear observer20–22 showed that the area under the ROC curve (AUC) for

the channelized Hotelling observer with Laguerre Gauss channels showed only a small improve-

ment with regularization. However, both SSIM and RMSE showed a large improvement. Our

preliminary results using human observer studies23,24 suggest a similar result in that there was no

large improvement with regularization for this task. The purpose of this work is to evaluate con-

strained reconstruction of undersampled MRI data using TV, wavelet, and a combination of these

constraints based on human observer performance in detecting a small signal in a 2-AFC task.

A model observer (S-DOG) is used to model human observer performance in this detection task.

Along with optimizing reconstruction, a goal of this work is also to reduce the number of future

human observer studies needed in undersampled MRI reconstruction by using model observers to

evaluate image quality.

2 Methods

2.1 Undersampled acquisition in MRI

For this study we consider 1-D undersampling of FLAIR images (Figure 1) with an acquisition

that samples every fourth phase encoding line plus fully sampling the middle 16 kspace lines

resulting in an effective undersampling factor of 3.48. Data used in the preparation of this article

were obtained from the NYU fastMRI Initiative database.25 The average white matter signal to

noise ratio (SNR) for the fully sampled multi-coil SENSE reconstructions (R=1) was measured by

estimating the standard deviation from components of the image with only noise and assuming a

Rayleigh distribution26 and the mean signal across a homogeneous region of white matter image

in the reconstructed slices. This led to an average white matter SNR of 83 in the 50 slices used

for the observer studies. The NYU fastMRI investigators provided data but did not participate in

analysis or writing of this report.

Fig 1 (A) Sampling mask for 4x undersampling, (B) Fully sampled image, (C) Undersampled constrained reconstruc-

tion with no TV regularization, Aliasing in the vertical axis is visible in the undersampled image. The acquisition had

a 2x oversampling in the horizonal direction.

2.2 Constrained Reconstruction from multi-coil Data

Constrained reconstruction minimizes a data agreement functional with additional constraints. For

this work we consider a total variation and wavelet constraint16 and multi-coil parallel imaging

using SENSE27 with the coil sensitivities estimated using the sum of squares method which leads

to real estimates of real-valued objects.

The following functional was minimized when reconstructing these images:

||H(f)−g||2

2+αΨ||Ψ(f)||1+αT V ||∇f||1,(1)

where H(f)is the undersampled Fourier operator acting on the discretized object f, the Fourier

data is g,Ψis the Daubechies 4 wavelet transform, ||∇f||1is the L1norm of the gradient which

is the total variation operator and αΨand αT V are the regularization parameters for the wavelet

and TV constraints respectively.16 Sample images with different amounts of TV and wavelet reg-

ularization are shown in Figure 2and Figure 3respectively. The reconstruction of the images was

done using the Berkeley Advanced Reconstruction Toolbox (BART) toolbox.28 The ensemble root

mean squared error for the reconstructed images (ERMSE) was computed using the fully sampled

unregularized reconstruction normalized to [0,1] as the reference image. The underampled recon-

structions were normalized to [0,1] before computing the RMSE. The ERMSE was computed from

50 slices from 5 volumes.

Fig 2 Sample undersampled images reconstructed with TV regularization, A) αT V = 0.01, B) αT V = 0.02, C)

αT V = 0.05, D) αT V = 0.1. As the regularization increases, there are reduced aliasing artifacts but also reduced

resolution. The arrow in image A shows the location of one of the undersampling artifacts.

2.3 Two-alternative forced choice experiments

In each individual trial of the 2AFC experiment we presented three 128x128 pixel images: one

image of an anatomical background with the signal, the signal, and one image of an anatomical

background without the signal. The signal image was always in the center, and the location (left

or right) of the anatomical image with the signal was randomly chosen for each trial. All images

are scaled to [0,1] before being displayed using the 8 bit gray scale colormap in MATLAB. Since

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Modelinghumanobserverdetectioninundersampledmagneticresonanceimaging(MRI)reconstructionwithtotalvariationandwaveletsparsityregularizationAlexandraG.O'Neilla,EmelyL.Valdeza,SajanGoudLingalab,AngelR.Pinedaa,*aManhattanCollege,DepartmentofMathematics,4513ManhattanCollegePkwy,TheBronx,NY,USA,10471bUnive...

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Modeling human observer detection in undersampled magnetic resonance imaging MRI reconstruction with total variation and wavelet sparsity regularization

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