Model-based optoacoustic inversions with incomplete projection data
(a) Reconstructable (bright solid line) and “invisible” (bright dashed line) boundaries of a round object with a square insertion partially lying in the “visibility region” (shaded area) and the “invisibility domain” for a detector moving along the dark solid arc. Dashed boundaries blur away since they do not fulfill detection criterion, i.e., they do not have a normal passing at least through one detector position. (b) Backprojection reconstruction of the phantom shown in (a). Boundaries that do not fulfill the detection criterion blur away. (c) The condition number of the matrix as a function of the detection arc. The higher the condition number, the more error-prone the inversion of becomes. (d) IMMI reconstruction of the phantom. IMMI reconstructions show stripe artifacts in the invisibility domain.
(a) Phantom containing an insertion similar to the stripe artifacts in the “invisibility” domain. (b) The energy of its optoacoustic signal as a function of the detector position indicating a high directivity. As a result, the optoacoustic signal of such structures cannot be detected in limited-view detection scenarios with a detection arc smaller than 190° and, consequently, has minute effect on the mean square error in Eq. (6) which is minimized in order to obtain an image. Any form of numerical or experimental inaccuracies may therefore be misinterpreted by the optimization algorithm as originating from such objects.
(a) The RMSD between reconstruction and original images for the four phantoms shown as insets in a 170° limited-view scenario for the TGSVD method. For all the phantoms, the minimum RMSD is obtained approximately for the same number of SVs used in the reconstruction. Consequently, one can determine the number of SVs used in the reconstruction a priori in a simulation study based on an arbitrary phantom. (b) The RMSD between PLSQR reconstruction and solution and the corresponding residual error for 170° reconstructions with noisy data as a function of the iterations. Since the method is only slightly semiconvergent, the relative change in can be used to devise a stopping criterion. The two inlays show the contribution of the iteration after the minimum of the RMSD has been reached, for the LSQR and the PLSQR algorithm. Stopping the iterations leads to a loss of image relevant low frequency information for the LSQR method, which is not the case for the PLSQR method.
(a) The phantom used in the numerical study representing the map of local laser energy deposition as well as the detection arc on which the virtual transducer is assumed to rotate around the sample. (b) RMSD between the unregularized reconstruction and the solution for different detection arcs and noise levels. [(c) and (d)] RMSD for the TGSVD method and the PLSQR algorithm. Both methods yield results of similar accuracy. The increase in the RMSD is due to the blurring of boundaries not fulfilling the detection criteria and not due to the stripe artifacts.
[(a)–(c)] Unregularized reconstructions of the phantom shown in Fig. 4(a) based on 240°, 170°, and 120° detection arcs and 8 dB SNR. For detection arcs smaller than 190°, strong stripe artifacts appear, which mask the underlying object features. [(d)–(f)] PLSQR and [(g)–(i)] TGSVD reconstructions for the same detection arcs and the same SNR of 8 dB. Both techniques reduce the stripe artifacts; however, the blurring of boundaries is still present for detection arcs smaller than 180°. [(j)–(l)] Backprojection based reconstructions. They are obviously not quantitative and also suffer from the blurring of boundaries.
Reconstructions of a complex phantom representing mouse anatomy. (a) IMMI full-view reconstruction of a mouse phantom with noisy data (SNR of 8 dB). (b) IMMI without regularization, (c) PLSQR regularized, and (d) backprojection reconstruction in a 170° detection geometry. The arrows indicate the blurred boundaries due to the limited-view detection geometry.
Experimental reconstruction from a quadratic insertion embedded in a homogeneous scattering and slightly absorbing cylindrical background. The columns correspond to the following detection arcs: 360°, 170°, and 120°; the rows to unregularized [(a)–(c)], PLSQR [(d)–(f)], and TGSVD [(g)–(i)] regularized IMMI reconstructions, and [(j)–(l)] to backprojection reconstructions. IMMI reconstruction without regularization show strong stripe artifacts, which mask the underlying structures; regularization techniques allow correction. Both IMMI and backprojection reconstructions suffer from the blurring of boundaries not fulfilling the detection criteria.
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