Scintigraphy is a common nuclear medicine method to image molecular target’s bio-distribution and pharmacokinetics through the use of radiotracers and gamma cameras. The patient’s images are obtained by using a pair of opposing large flat gamma ray detectors equipped with parallel-hole lead or tungsten collimators that preferentially detect gamma-rays that are emitted perpendicular to the plane of the detector. The resulting images form an anterior/posterior (A/P) planar image pairs. The obtained images are contaminated by noise and contain artifacts caused by gamma-ray attenuation, collimator penetration, scatter and other detrimental factors. Post-filtering of the images can reduce the noise, but at the cost of spatial resolution loss, and cannot remove any of the aforementioned artifacts. In this study, we introduced a new image reconstruction-based method to recover a single corrected planar scintigraphic patient image corrected for attenuation, system spatial resolution and collimator penetration, using the A/P image pair (two conjugated views) as data. To accomplish this task, we used a system model based on the gamma camera detectors physical properties and applied regularization method based on sparse image representation to control noise while preserving spatial resolution. In this proof-of-concept study, we evaluated the proposed approach using simple numerical phantoms. The images were evaluated for simulated lesions images contrast and background variability. Our initial results indicate that the proposed method outperforms the conventional methods. We conclude, that the proposed approach is a promising methodology for improved planar scintigraphic image quality and warrants further exploration.
Wavelet transforms have been successfully applied in many fields of image processing. Yet, to our knowledge, they have never been directly incorporated to the objective function in Emission Computed Tomography (ECT) image reconstruction. Our aim has been to investigate if the ℓ1-norm of non-decimated discrete cosine transform (DCT) coefficients of the estimated radiotracer distribution could be effectively used as the regularization term for the penalized-likelihood (PL) reconstruction, where a regularizer is used to enforce the image smoothness in the reconstruction. In this study, the ℓ1-norm of 2D DCT wavelet decomposition was used as a regularization term. The Preconditioned Alternating Projection Algorithm (PAPA), which we proposed in earlier work to solve penalized likelihood (PL) reconstruction with non-differentiable regularizers, was used to solve this optimization problem. The DCT wavelet decompositions were performed on the transaxial reconstructed images. We reconstructed Monte Carlo simulated SPECT data obtained for a numerical phantom with Gaussian blobs as hot lesions and with a warm random lumpy background. Reconstructed images using the proposed method exhibited better noise suppression and improved lesion conspicuity, compared with images reconstructed using expectation maximization (EM) algorithm with Gaussian post filter (GPF). Also, the mean square error (MSE) was smaller, compared with EM-GPF. A critical and challenging aspect of this method was selection of optimal parameters. In summary, our numerical experiments demonstrated that the ℓ1-norm of discrete cosine transform (DCT) wavelet frame transform DCT regularizer shows promise for SPECT image reconstruction using PAPA method.
We arrived at the fixed-point formulation of the total variation maximum a posteriori (MAP)
regularized emission computed tomography (ECT) reconstruction problem and we proposed an
iterative alternating scheme to numerically calculate the fixed point. We theoretically proved that
our algorithm converges to unique solutions. Because the obtained algorithm exhibits slow convergence
speed, we further developed the proximity algorithm in the transformed image space, i.e.
the preconditioned proximity algorithm. We used the bias-noise curve method to select optimal
regularization hyperparameters for both our algorithm and expectation maximization with total
variation regularization (EM-TV). We showed in the numerical experiments that our proposed
algorithms, with an appropriately selected preconditioner, outperformed conventional EM-TV algorithm
in many critical aspects, such as comparatively very low noise and bias for Shepp-Logan
phantom. This has major ramification for nuclear medicine because clinical implementation of our
preconditioned fixed-point algorithms might result in very significant radiation dose reduction in
the medical applications of emission tomography.