Efficient non-negative constrained model-based inversion in optoacoustic tomography

Abstract

The inversion accuracy in optoacoustic tomography depends on a number of parameters, including the number of detectors employed, discrete sampling issues or imperfectness of the forward model. These parameters result in ambiguities on the reconstructed image. A common ambiguity is the appearance of negative values, which have no physical meaning since optical absorption can only be higher or equal than zero. We investigate herein algorithms that impose non-negative constraints in model-based optoacoustic inversion. Several state-of-the-art non-negative constrained algorithms are analyzed. Furthermore, an algorithm based on the conjugate gradient method is introduced in this work. We are particularly interested in investigating whether positive restrictions lead to accurate solutions or drive the appearance of errors and artifacts. It is shown that the computational performance of non-negative constrained inversion is higher for the introduced algorithm than for the other algorithms, while yielding equivalent results. The experimental performance of this inversion procedure is then tested in phantoms and small animals, showing an improvement in image quality and quantitativeness with respect to the unconstrained approach. The study performed validates the use of non-negative constraints for improving image accuracy compared to unconstrained methods, while maintaining computational efficiency.

Constrained Inversion and Spectral Unmixing in Multispectral Optoacoustic Tomography

“…The constrained reconstruction (CR) and the constrained combined problems (CB1 and CB2) were solved using an efficient iterative non-negative least squares method introduced in [32]. On the other hand, the constrained unmixing problems (CM) defined in (15) were solved with the FNNLS method [37], which, due to the small dimensionality of this problem, is more efficient.…”

“…a non-negative constrained inversion has been shown to render images free of negative ab- sorption values [31]. We have also recently demonstrated that non-negative constrained inversion of a linear two-dimensional optoacoustic tomographic model can further enhance quantitative performance by yielding reconstructed values proportional to the actual absorption coefficient [32]. …”

On the link between the speckle free nature of optoacoustics and visibility of structures in limited-view tomography

“…In both cases, the theoretical signals were calculated for 1000 instants at 37.5 MSPS and subsequently band-pass filtered between 25 kHz and 5 MHz prior to applying the model-based reconstruction. In this case, a non-negative constraint was also incorporated in the inversion procedure [33]. The resulting images obtained with the same 90° and 270° arrays shown in Fig.…”

Maximum Entropy Based Non-Negative Optoacoustic Tomographic Image Reconstruction

“…al. [13] compared the utility of different minimization procedures using non-negative constraints, including steepest descent, conjugate gradient, and quasi-newton based inversion. Typical non-negative constraint schemes truncate the negative values within each step of the gradient iteration, forcing a result containing only positive or zero values.…”

“…For example, 2 -or 1 -norm minimization of the total variation of an image minimizes the edges of the reconstructed image. Using this notion, negative artifacts can then be eliminated by applying an explicit non-negativity constraint along with 2 -norm minimization [13], [15]. Another image metric that has been considered for eliminating negative values is the entropy of an image [16], [17].…”