How is the first image estimate generated in CT scan iterative reconstruction (IR)?

Background info:

For decades CT scanners produced medical images from x-rays travelling through the tissues of the patient at different angles through analytical methods based on the Radon transform and Fourier slice theorem, and generally falling under the category of filtered backprojection (FBP), beautifully illustrated by Adam Kesner:

and Wikipedia:

This is nicely explained here.

These had limitations, such as the presence of sparse matrices with logarithmic transformations. The need for logarithmic transformation of the acquired data stems from the fact that the projected data $I_d$ at a given angle is proportional to the exponential of the integral of the attenuation along the x-ray beam

$$I_d= I_0 expleft[- int_0^d mu(s; bar E) mathrm dsright],$$

where $mu$ is the linear attenuation coefficient, which depends on location $s$ and effective energy $bar E,$ and hence, the log transformation is part of the generation of the 2D FT of the image. In iterative reconstruction the log transformation of the data comes about when calculating the maximum posterior estimate of the line integrals along different angles based on detected x-ray intensity, which is handled as log-likelihood problems. Sparse matrix issues may surface on the final image as artifact, which was basically addressed by increasing the dose delivered to the patient.

Iterative reconstruction came about as an attempt at applying computer-intensive optimization processes to handling problems such as the noise in the image, and with the ultimate goals of either improving the diagnostic image, or reducing dose. These IR techniques seem to be referred as either hybrid IR models (iDose (Philips) or ASiR (GE)) or model-based reconstruction (MBIR) (or "pure" IR). In both cases there is an objective or cost function and coefficients to be estimated, typically with a penalized regression model. This regression or optimization process is logically solved computationally (similar to gradient descent). The distinction between IR models is difficult to understand, but it seems as though initial IR products (ie Philips iDose would improve images based on a penalized regression model for weightings of noisier measurements based on photon distribution statistics. MBIR, on the other hand, would take into consideration the x-ray anode and receptor geometry and optics to produce a "forward projection on an assumed starting image."

In this great 2018 review paper on regularization techniques by Hao Zhang, the distinction between hybrid and model based seems to have been rendered obsolete in favor of SIR (Statistical Image Reconstruction) (please note that LDCT stands for low-dose CT scan):

in contradistinction to FBP ("analytical") or ART ("algebraic").

In general model-based IR seems to take statistical IR to a different level, incorporating neural networks, as well as adding more refined assumptions such as the optics of the receptors, etc. Largely, though, these are proprietary algorithms, which are not available to the public or the medical community.

---

Question:

The question is in the end very basic, and makes reference to the terminology and general process used in the diagram found in this review paper:

and specifically

whether the $color{red}{text{“First image estimate”}}$ would (implied in the text) seem to be generated as an reconstruction process similar to FBP.

If this is remotely correct, my understanding of the picture above could be reworded as follows:

The projection data gathered by the continuously spiraling x-ray beam passing through the patient forms the projected data or sinogram (which is visualized as a gray, vertically directed spiral or sine wave) containing the raw data. So far this is the "forward projection" (yellow arrow in the image below). The second step consists of
$$begin{align}
&color{red}{text{a backprojection}}\
&color{red}{text{to get a rough picture}}\
&color{red}{text{with the same methods}}\
&color{red}{text{used in filtered backprojection (FBP) (?)}}
end{align}$$
(corresponding to the red arrow in the picture below), which is later optimized progressively by pretending to extract from this rough picture a sinogram ("simulated fwd projection" in the image below), and comparing it to the initial sinogram:

From everything above it would seem like hybrid IR algorithms would start off from a FBP of the raw data in the sinogram, while in the MBIR algorithms the first step would be simulated forward projection from a set of assumptions.

So the most complete formulation of the question would be whether the "first image estimate" in hybrid IR algorithms is formed via FBP; and how the "simulated forward projection" is obtained in MBIR algorithms.

---

Online available references:

1. Recent Advances in CT Image Reconstruction, J. Hsieh

2. Using Algebraic Reconstruction in Computed Tomography, N. Tang

3. Regularization strategies in statistical image reconstruction of
   low-dose x-ray CT: A review, H. Zhang

4. iDose Iterative Reconstruction Technique, Philips info

5. State of the Art: Iterative CT Reconstruction Techniques, L. Geyer

6. Algebraic Reconstruction Algorithms Basics of Image Reconstruction