Accelerated Compressed Sensing Based CT Image Reconstruction

<div>Simulation results for a Shepp-Logan phantom. The bottom row shows an expanded view of the region marked in panel (a). (a) Original phantom image. Reconstructions using 128 projections with (b) inverse PPFT-based Radon transform (normalized error <svg height="8.63352pt" id="M189" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -8.38798 26.893 8.63352" width="26.893pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M537 353L508 390C487 357 455 333 417 333C389 333 344 353 309 370C265 391 212 414 172 414C122 414 79 382 50 340L81 307C101 339 134 364 172 364C198 364 245 343 280 326C324 305 375 283 417 283C466 283 507 314 537 353ZM537 168L508 205C487 172 455 148 417 148C389 148 344 168 309 185C265 206 212 229 172 229C122 229 79 197 50 155L81 122C101 154 134 179 172 179C198 179 245 158 280 141C324 120 375 98 417 98C466 98 507 129 537 168Z" id="g117-132"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.263,0)"><path d="M241 635C89 635 35 457 35 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vert-adv-y="480"></glyph.data></g></svg>), (c) an iterative soft thresholding based method without considering EAW (normalized error <svg height="11.773pt" id="M190" style="vertical-align:-0.2454996pt" version="1.1" viewbox="-0.0498162 -11.5275 34.4452 11.773" width="34.4452pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M537 353L508 390C487 357 455 333 417 333C389 333 344 353 309 370C265 391 212 414 172 414C122 414 79 382 50 340L81 307C101 339 134 364 172 364C198 364 245 343 280 326C324 305 375 283 417 283C466 283 507 314 537 353ZM537 168L508 205C487 172 455 148 417 148C389 148 344 168 309 185C265 206 212 229 172 229C122 229 79 197 50 155L81 122C101 154 134 179 172 179C198 179 245 158 280 141C324 120 375 98 417 98C466 98 507 129 537 168Z" id="g117-132"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g 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Rebinned parallel rays were used in all three methods to reconstruct the image.</div>

Computational and Mathematical Methods in Medicine

Accelerated Compressed Sensing Based CT Image Reconstruction

Figure 7