Wednesday, February 15, 2012

"Les Caméras Aléatoires" and Nuit Blanche's Mailbag

Tomorrow night (Thursday), I'll be speaking at Dorkbot at La Cantine and it'll be at 8:00 pm. The title of the talk will be "Les Caméras Aléatoires". The crowd is not made up of specialists but some of the folks  are interesting hardware hackers and artists and so I'll be pitching the random lens imager. If you want to have a bird's eye view of the subject, you might consider attending. I think I'll be speaking in French (depending on the crowd).

Today Gabriel Peyre:and Dick Gordon: provided some insights in a simplified approach to TV regularization and the use of FBP in hardware (CT scanners). While I realize that FBP does not work in 3D, there ought to be a simple case made that connects FBP to compressive sensing simply. At the very least, additional insight could definitely be gained from taking into account the findings of the intriguing paper A variant on the compressed sensing of Emmanuel Candes by Yves Meyer and Basarab Matei, but that's just me. Without further wait here are the following insights:

From Gabriel Peyre:

Hi everybody,
... I have finally taken some time to explain how to solve TV regularization without using primal-dual-schemes:
(it is applied to segmentation, but you can apply the same method to inverse problems as well).
If you find any error or typo, please let me know!
For another approach to avoid using primal dual schemes:

From Dick Gordon:

Dear Igor, 
There’s a new iterative CT algorithm in the mill: SAFIRE (Sinogram Affirmed Iterative Reconstruction), which I came across in: Siemens (2012). Flash Speed. Lowest Dose. SOMATOM Definition Flash  
It’s described in: 
Nelson, R.C., S. Feuerlein & D.T. Boll (2011). New iterative reconstruction techniques for cardiovascular computed tomography: How do they work, and what are the advantages and disadvantages? Journal of Cardiovascular Computed Tomography 5(5), 286-292.
Abstract. The radiation doses associated with diagnostic CT scans has recently come under scrutiny. In the process of developing protocols with lower doses, it has become apparent that images reconstructed with a filtered back projection (FBP) technique are often inadequate. Although very fast and robust, FBP images are prone to high noise, streak artifacts and poor low contrast detectability in low dose situations. Manufacturers of CT equipment have responded to this limitation by developing new image reconstruction techniques that derive more information from the data set. These techniques are based on the use of maximum likelihood algorithms and are referred to at iterative reconstructions. This iterative process can be used on the slice data alone, a combination of raw and slice data or on the raw data alone. The latter approach, which is referred to as model based iterative reconstruction, is the most computationally demanding as it models the entire process, from the shape of the focal spot on the anode, the shape of the emerging x-ray beam, the three-dimensional interaction of the beam with the voxel in the patient and the two-dimensional interaction of the beam with the detector. This article discusses the fundamentals of iterative reconstruction techniques, the pros and cons of the various manufacturer approaches and specific applications, especially to cardiovascular CT. 
Beister, M., D. Kolditz & W.A. Kalender (2012). Iterative reconstruction methods in X-ray CT. Physica Medica,
Abstract: Iterative reconstruction (IR) methods have recently re-emerged in transmission x-ray computed tomography (CT). They were successfully used in the early years of CT, but given up when the amount of measured data increased because of the higher computational demands of IR compared to analytical methods. The availability of large computational capacities in normal workstations and the ongoing efforts towards lower doses in CT have changed the situation; IR has become a hot topic for all major vendors of clinical CT systems in the past 5 years.
This review strives to provide information on IR methods and aims at interested physicists and physicians already active in the field of CT. We give an overview on the terminology used and an introduction to the most important algorithmic concepts including references for further reading. As a practical example, details on a model-based iterative reconstruction algorithm implemented on a modern graphics adapter (GPU) are presented, followed by application examples for several dedicated CT scanners in order to demonstrate the performance and potential of iterative reconstruction methods. Finally, some general thoughts regarding the advantages and disadvantages of IR methods as well as open points for research in this field are discussed. 
Nothing explicitly on compressive sensing in these. SAFIRE is basically iteration of FBP (Fourier backprojection), and so will suffer the same problems that FBP has with sparse data. Nevertheless, the fact that it has been embedded in a commercial CT scanner and received FDA approval for 50% dose reduction may invigorate the search for sparse CT algorithms that retain image quality while further reducing patient dose...... 
Yours, -Dick
Dr. Richard (Dick) Gordon
Theoretical Biologist, Embryogenesis Center
Gulf Specimen Marine Laboratory ( 

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