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Image Processing Project Tomographic Image Reconstruction Introduction This presentation will cover a brief description of tomographic imaging, image reconstruction methods, and design challenges. 1. Tomography 2. Image Reconstruction 3. Design Challenges 4. Your Project 2 Background: Importance of Medical Imaging There are an estimated 630,000 imaging procedures every week in the US. The average radiologist has a case load around 35% higher than just 5 years ago. “Molecular imaging holds great promise for early detection and treatment of numerous diseases, for providing researchers with detailed information about cellular physiology and function, and for facilitating the goal of personalized medicine.” – NIH roadmap 3 Modern imaging modalities cover the EM spectrum and all scales of resolution. Organism Organs Tissue Cells Proteins Genes 4 Tomography X-ray CT Scanner X-ray CT Images of the Human Abdomen 5 Tomography means to image using sections or slices, tomo is Greek for cut, graph means form (plot) an image. Tomograms can be created using a variety of physical mechanisms X-ray Attenuation Nuclear Magnetic Resonance Position-Electron Annihilation Ultrasound Interactions Modalities X-ray Computed Tomography Magnetic Resonance Imaging Positron Emission Tomography Ultrasound Interactions 6 To do Tomography, we need to have many projections from different angles. Transforms the object we are imaging to a Sinogram 7 Forming the Sinogram 8 y = density of 0 = density of 25 x = density of 50 (x, y) 9 y = density of 0 y1 = density of 25 x1 x = density of 50 (x 1,y1) 50 10 y = density of 0 = density of 25 x = density of 50 (x, y) 11 (x, y) = density of 25 = density of 50 y x 12 (x, y) = density of 25 = density of 50 13 (x, y) = density of 25 = density of 50 Our First Projection 14 (x, y) = density of 25 = density of 50 P(t) t Our First Projection 15 (x, y) = density of 25 = density of 50 P(t) t Our First Projection 16 (x, y) = density of 25 = density of 50 P 0 (t) t Our First Projection 17 = density of 25 (x, y) = density of 50 P 0 (t) t t Our First Projection 18 P 45 (t) 45 o t t Our Second Projection 19 P 90 (t) t 90 o t Our Third Projection 20 t Sinogram 21 t Sinogram 22 t Sinogram 23 t Sinogram 24 t Sinogram 25 t Sinogram 26 t Sinogram 27 t Sinogram 28 t Sinogram 29 t Sinogram 30 t Sinogram 31 t Sinogram 32 t Sinogram 33 t Sinogram 34 t Sinogram 35 t Sinogram 36 t Sinogram 37 t Sinogram 38 Given all these projections, how do we reconstruct the tomogram? Filtered Backprojection 39 Image Reconstruction Using Filtered Backprojection P (t) Filter t Backprojection 40 Backprojection Backprojection “smears” the data back. fˆ (x, y) f (x, y) 41 Backprojection Backprojection “smears” the data back. fˆ (x, y) f (x, y) 42 Backprojection Backprojection “smears” the data back. infinite number of projections fˆ (x, y) f (x, y) 43 Filtered-Backprojection If we filter the projections before backprojection we can recover the original object. fˆ (x, y) f (x, y) 44 Filtering the projection Filtering is a basic operation in signal processing. Spatial or Temporal domain filtering (convolution) Frequency domain filtering Lets consider spatial domain filtering: g(t) (P h)(t) P( )h(t ) input signal (projection) filtered signal filter kernel convolution operator 45 TPS: Think-Pair-Share Match up the following Sinograms with their objects O1 S1 O? = S? O2 S2 O3 S3 46 Design Challenges In cases where the projection is taken using x-rays, there is a risk associated. x-rays absorbed by the body can cause damage to DNA directly or through the formation of free radicals. The larger the number of projections and the longer the x-rays are on, the higher the dose delivered to the patient. There is a fundamental tradeoff between dose, the number of projections, and the noise in the projections. 47 Basics of Radiation Biology We are constantly exposed to naturally occurring radiation (radon, cosmic rays) about 3 milli-Sieverts per year there is some evidence that anti-oxidants, found in fruits and vegetables, can protect cells from free radical formation A single chest x-ray is equivalent to about 10 days of natural exposure A whole-body x-ray CT exam is equivalent to about 3 years of equivalent natural exposure 48 Radiation Monitoring OSHA requires all those who work with radiation to be badged and monitored for dose. 49 Noise in X-rays X-ray images are formed by counting the number of photons leaving the subject compared to those entering. The count is a random variable that is Poisson distributed. 50 Dose and Image Quality The longer the X-rays are on the lower the noise level but the higher the dose. Image Quality Contrast-to-Noise ratio improve by averaging multiple projections Total Dose Number of projections*dose per projection increases linearly with the number of averages 51 Contrast to Noise Ratio CNR measures how much contrast compared to noise there is in the reconstructed image 1 2 CNR 2 2 1 2 Region 1 Region 2 1 250.1 1 70.3 2 191.9 2 206.1 CNR 3.5 52 Total Dose The dose delivered is a complex formula that depends on the geometry and the exact characteristics of the x-rays (energy etc). To compare different tomographic image acquisitions we will use a simple formula to estimate the total dose D(N) N * d where N is the number of projections and d is the (fixed) dose per projection. 53 Your Project There are two parts to this project. Part I Generating projections - students will use Matlab to simulate projection images from a phantom with varying numbers of projections. Image Reconstruction - students will use Matlab to reconstruct the images using filtered backprojection. You will also use Matlab to add noise to the projections to simulate the effect of photon counting and explore the effect on image reconstruction quality. 54 Your Project There are two parts to this project. Part II Given two sinograms, one with a simulated “tumor”, you will experimentally determine which sinogram contains the tumor using different reconstruction filters. 55