Computed Tomography Image Reconstruction

Reconstruction Input: Raw Data 255 199 712 Intensity (transmission) measurements 534 417 364 501

Image Reconstruction Output: Image Data Individual pixel values (question marks) ?

Algorithm Set of calculation rules for getting a specific output (answer) from a specific input Reconstruction algorithm examples Back projection Filtered back projection Interpolation

Back Projection Reconstruction 63 ? ? ? ? ? ? ? Reconstruction Problem converting transmission data for individual projections into attenuation data for each pixel

Back Projection Reconstruction for given projection, assume equal attenuation for each pixel repeat for each projection adding results 63 9 9 9 9 9 9 9

Back Projection Reconstruction Assume actual image has 1 hot spot (attenuator) Each ray passing through spot will have attenuation back-projected along entire line Each ray missing spot will have 0’s back-projected along entire line 63 Hot Spot 9 9 9 9 9 9 9

Back Projection Reconstruction Each ray missing spot stays blank Each ray through spot shares some density Location of spot appears brightest 63 9 9 9 9 9 9 9 Hot Spot

Back Projection Reconstruction Streaks appears radially from spot star artifact Star Artifact Spokes Hot Spot

Filtered Back Projection * enhancement of back projection technique filtering function (convolution) is imposed on transmission data small negative side lobes placed on each side of actual positive data negative values tend to cancel star artifact Unfiltered back projection Filtered back projection

Filtered Back Projection Operationally fast reconstruction begins upon reception of first transmission data Commercially used reconstruction algorithm for decades Now being replaced by iterative

“It All Adds Up” Puzzle www.education-world.com/a_lesson/italladdsup Iterative Reconstruction “It All Adds Up” Puzzle www.education-world.com/a_lesson/italladdsup 17 2 5 6 4 9 1 22 16 19 7 9 23 15 17 14

This is what your CT Scanner must solve! 13 Slightly harder? 22 12 10 15 16 22 11 10 17

Real Problem Slightly More Complex *** 100’s of diagonals @ 100’s of angles 14 512 values 512 values m11 m12 m13 m14 m21 m22 m23 m24 m31 m32 m33 m34 m41 m42 m43 m44 35 13 22 9 24 13 15 22 16

Iterative Reconstruction calculate difference between measured & calculated attenuation for next projection correct pixels equally for current projection to achieve measured attenuation BUT!!!

Iterative Reconstruction Correcting pixels for one projection alters previously-calculated attenuation for others corrections repeated for all projections until no significant change / improvement

Iterative Reconstruction Start with measured data 12 15 9 24 12 12 ? ? ? ? ? ? ? ? ? 17 19 12 Measurements

Iterative Reconstruction Make initial guess for first projections by assuming equal attenuation for each pixel in a projection Similar to back projection 12 15 9 Measurements 24 12 12 24 12 12 8 4 4 ? ? ? ? ? ? ? ? ? 17 19 12 Initial guess based upon vertical projections Measurements

Iteration Example 8 4 4 24 12 12 Initial guess based 8 4 4 24 12 12 Initial guess based upon vertical projections 8.33 4.33 4.33 9 5 5 6.67 2.67 2.67 17 19 12 Low by 1; add .33 to each. Make corrections based on horizontal Projections data Low by 3; add 1 to each. High by 4; subtract 1.33 from each.

Iteration Example 8.33 4.33 4.33 9 5 5 6.67 2.67 2.67 17 19 12 9 15 8 4.16 4.33 9.17 4.33 4.83 6.67 2.84 2.33 12 Make corrections based upon Data measured on diagonals High by .33; subtract .17 from each. High by 1; subtract .33 from each. Low by .3; add .17 to each.

Iterative Reconstruction: General Electric Adaptive Statistical Iterative Reconstruction (ASIR) Claims & Observations 22-66% reduction in dose in abdominal scans with no change in spatial or temporal resolution Algorithm creates different texture Appears artificial Creates a “new normal”

Iterative Reconstruction: Siemens Iterative Reconstruction in Image Space (IRIS) Claims & Observations Dose reduction up to 60% without quality loss Fast reconstruction

Iterative Reconstruction: Philips iDose Claims & Observations Dose reduction for coronary CT angiography more than 80% without quality loss Reconstruction times of up to 20 images/second Can improve image quality in typically high noise bariatric exams

Multi-plane reconstruction using data from multiple axial slices it is possible to obtain sagittal & coronal planes oblique & 3D reconstruction Non-spiral reconstruction Poor appearance if slice thickness >>pixel size multi-plane reconstructions are computer intensive

3D Reconstructions Uses pixel data from multiple slices Algorithm identifies surfaces & volumes Display renders surfaces & volumes Real-time motion auto-rotation user-controlled multi-plane rotation

3D Reconstructions