Automated Aperture GenerationQuantitative Evaluation of Ape

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1 . Objectives Approaches Randomness Reconstructing Images from K-space References Automated Aperture Generation Quantitative Evaluation of Aperture April 5, 011

2 . Objectives Approaches Randomness Reconstructing Images from K-space References The objective is to show specific apertures can be used for scans to produce better results than always using a random sampling method. + = =

3 . Objectives Approaches Randomness Reconstructing Images from K-space References One principle we are attempting to show computationally is a scaled down image will have a similar sensing matrix to its normal resolution image. Also, we want to show that slices of the body (similarly structured images) can benefit from the same aperture. Goal : Database of apertures shown to best random apertures for given images or similar images.

4 . Objectives Approaches Randomness Reconstructing Images from SprayK-space and PrayReferences Guided Matrix Construction Adaptive Approa Approach 1 : Random Generation and Testing

5 . Objectives Approaches Randomness Reconstructing Images from SprayK-space and PrayReferences Guided Matrix Construction Adaptive Approa In this approach we build matrices manually, see what works, and then attempt to improve the functioning of the given matrix. Doing this is time consuming. Prohibitively so. Other approaches are easily automated. This one was dropped pretty quickly, some example matrices

6 . Objectives Approaches Randomness Reconstructing Images from SprayK-space and PrayReferences Guided Matrix Construction Adaptive Approa Something that has interested me for a long time is genetic algorithms. Breeding off of the previous generations good or best results, comparing, improving, randomly adapting. With this approach we start with a few random matrices, and then test them. Whichever is best we breed off a new set and retest.

7 . Objectives Approaches Randomness Reconstructing Images from Pseudo K-space QuasiReferences Pseudo-random suggests closeness to the real thing by apparent sameness. So, a pseudo-random is similar to a real random distribution, because it attempts to appear random, however since it s algorithmically produced it can no be considered truly random.

8 . Objectives Approaches Randomness Reconstructing Images from Pseudo K-space QuasiReferences Quasi-random numbers don t clump like random/pseudo-random. In order to have a more uniform distribution each subsequently generated value don t have serial independence over previously generated values. Therefore in a finite set of points voids and clumps are avoided. Typically this distribution takes some work, but several good algorithms and implementations have taken the work out of it.

9 . Objectives Approaches Randomness Reconstructing Images from Compressive K-spaceSensing References What I ve Been Doing Prelim Conclusio With the reconstruction on the right, afourier transform. It is important for compressive sensing (CS) to note that most of the interesting bits in k-space are near the origin. There are some interesting bits further out, but they become much more sparse in relation to the increased distance from the origin.

10 . Objectives Approaches Randomness Reconstructing Images from Compressive K-spaceSensing References What I ve Been Doing Prelim Conclusio Reconstruction: full > LR > zf w/dc > CS from % k space samples sampling pattern

11 . Objectives Approaches Randomness Reconstructing Images from Compressive K-spaceSensing References What I ve Been Doing Prelim Conclusio All the samples are taken in a k-space representation, only the sample pattern and final reconstruction are shown here. The left most sampling pattern is a complete sample. Every pixel is sampled to reconstruct the exact starting image. The next image is reconstructed from an intense sampling around the origin. Most interesting, sparse, compressible images will have a increased density near the origin in their k-space representation. The final two are random sampling patterns. The second a less dense version of the first. Oversampling for reconstruction can lead to artifacts, under-sampling can lead to incomplete images. It s important to sample in certain areas, and to not sample too hard.

12 . Objectives Approaches Randomness Reconstructing Images from Compressive K-spaceSensing References What I ve Been Doing Prelim Conclusio Reconstruction: full > LR > zf w/dc > CS from % k space samples sampling pattern

13 . Objectives Approaches Randomness Reconstructing Images from Compressive K-spaceSensing References What I ve Been Doing Prelim Conclusio Weighted random sampling for the final two panels, increased sampling area in the second panel. Last, sparse panel with weighted center sampling shows better reconstruction

14 . Objectives Approaches Randomness Reconstructing Images from Compressive K-spaceSensing References What I ve Been Doing Prelim Conclusio Playing with methods of generating apertures Subtracting matrices to see whats working

15 . Objectives Approaches Randomness Reconstructing Images from Compressive K-spaceSensing References What I ve Been Doing Prelim Conclusio Saving a million images is annoying and infeasible. Quantitative best is bestish Test against similar images. I still like Monte Carlo methods more.

16 . Objectives Approaches Randomness Reconstructing Images from K-space References M. Lustig, D.L Donoho and J.M Pauly Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging Magnetic Resonance in Medicine, 007 Dec; 5(): Emmanuel Cands, Compressive sampling. (Int. Congress of Mathematics, 3, pp , Madrid, Spain, 00) Emmanuel Candes and Michael Wakin, An introduction to compressive sampling. (IEEE Signal Processing Magazine, 5(), pp. 1-30, March 00)