Solutions-2 Wiener Filter L( u) : PSD of inverse filter l(x) Sn ( u) : PSD of noise P ( u) : PSD of blurring filter p(x) S" ( u) : PSD of object P(u*) P(u)P(u*) = P ( u) 2 L(u) = 2 S ( u) ! P ( u) + n! "1 P(u*) S" ( u) L(u) = P(u) = 2 P ( u) P(u*) = 2 1 P ( u) + SNR(u) ! !
End of Deblurring Basics!!Now to discuss some real applications of Deblurring in CT
Jing Wang, Ge Wang, Ming Jiang Blind deblurring of spiral CT images Based on ENR and Wiener filterJournal of X-Ray Science and Technology – 2005[previous: IEEE Trans. on Medical Imaging 2003]
Blind Deconvolution P(u*) 1st Problem: L(u) = 2 S ( u) Finding P(u) P ( u) + n S" ( u) PSD of p(x) = ? P(u*) = 2 1 P ( u) + 2nd Problem: SNR(u) Finding SNR(u) SNR at different u = ?!
Solution to 1st ProblemAssume p(x) → Gaussian with σ = ? Deblur at multiple σ Find σ that gives best deblurring How to find best σ: Use ENR
Solution to 2nd Problem Assume SNR(σ) = k Find k by phantom studies
ENR• Edge to Noise Ration• in terms of I-divergence (Information Theoretic approach)• Noise effect• Edge effect• ENR = Edge effect / Noise effect
ENR Maximization Principle maximize ENR(σ,k) to get optimal σ
Rollano Hijarrubia et. al.Selective Deblurring for Improved Calcification Visualization and Quantification in Carotid CT Angiography: Validation Using Micro-CT IEEE Transactions on Medical Imaging 2009
Wiener Filter• Two problems to be solved: – 1. Point Spread Function (PSF) = ? – 2. Signal to Noise Ratio (SNR) = ?
Solution to 2nd Problem• Phantom designed• Scanned• Reconstructed• Deblurred at various SNR• Optimum SNR value chosen
Solution to 1st Problem• By measuring PSF of a bead image1• Resolution of scanner: 0.3 - 0.4mm Bead size: 0.28mm . Meinel JF, Wang G, Jiang M, et al. Spatial variation of resolution and noise in multi-detector row spiral CT. Acad Radiol. 2003;10:607– 613.
Selective Deblurring Axial MIPs (Maximum Intensity Projection) ofthe original, deconvolved, and restored images of the phantom.