Fast 3D image reconstruction method based on SVD decomposition of a block-circulant system matrix
Bibliographic record
Abstract
We propose an ultra-fast 3D image reconstruction method based on singular value decomposition (SVD) of a block-circulant system matrix obtained from a cylindrical image representation. PET and SPECT image reconstruction based on SVD of the system matrix has already been demonstrated previously but was limited to the reconstruction of small 2D images due to the difficulty of inverting an ill-conditioned large matrix. In this work, this difficulty is overcome by using a Fourier transformed factorization of the block-circulant matrix to accelerate the SVD decomposition procedure and make it more robust. The Fourier transform is further used to accelerate the matrix-vector operations between the system matrix pseudo-inverse and the projection data resulting in an extremely fast direct image reconstruction method. A maximum acceleration of the method is achieved by taking advantage of all in-plane and axial symmetries between the tubes of response through the use of a 3D cylindrical image representation preserving all symmetries in the system matrix. Using the same projection data, the proposed method delivers images of visual quality comparable to FBP, but 25 times faster. Moreover, for imaging systems with many symmetries, the method is so fast that it can produce higher quality images using all available 3D projection data, taking time comparable to FBP or MLEM, the latter using single plane, i.e. partial 2D projection data only. The new method is therefore ideal for real time 3D image reconstruction allowing for the instant visualization of the image estimate while the patient is being scanned.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".