Exponential filtering of singular values improves photoacoustic image reconstruction

Exploring polynomial based interpolation schemes for photoacoustic tomographic image reconstruction

Photoacoustic tomography (PAT) imaging employing polynomial-based interpolation methods is discussed. Nearest-neighbor, bilinear, bicubic and biquintic algorithms were implemented for the construction of the model matrix, and images were formed using the Tikhonov regularization and total variation (TV) minimization procedures. The performance of the interpolation methods was assessed by comparing the reconstructed images of three numerical and two experimental phantoms. The numerical and experimental studies demonstrate that the performance of the interpolation schemes is nearly equal for large PA sources. The simplest nearest-neighbor technique provides better image reconstruction for a sparse source compared to the others. The nearest-neighbor protocol may be adopted in practice for vascular imaging using PAT.

Photoacoustic Signal Simulation Using Discrete Particle Approach and its Application in Tomography

A theoretical framework for photoacoustic (PA) signal simulation using a discrete particle approach is discussed, and the tomographic image reconstruction using such signals is reported. Various numerical phantoms in two dimensions were constructed by inserting monodisperse/polydisperse solid circles/disks of uniform strength occupying regular or random locations within the imaging region. In particular, a blood vessel network phantom was simulated by positioning solid circles mimicking red blood cells randomly within the vessel using a Monte Carlo method. The PA signal from a single disk was obtained by numerically evaluating the analytical formula, and then, such signals from many disks were summed up linearly to generate the resultant signals at detector locations. Classical backprojection and time-reversal algorithms were employed to form reconstructed images. Two model-based approaches, namely impulse response-based (IRB) and interpolation-based (IPB) methods, were also deployed for image reconstruction. Some standard parameters were calculated to assess the performance of these reconstruction algorithms. The simulation results demonstrate that the Monte Carlo method can be applied in practice for the fast simulation of tissue realization keeping microscopic details intact, and accordingly, PA signals can be calculated for photoacoustic tomography (PAT) imaging. Furthermore, the IRB technique produces images with superior quality and outperforms other algorithms.

Dimensionality reduced plug and play priors for improving photoacoustic tomographic imaging with limited noisy data

The reconstruction methods for solving the ill-posed inverse problem of photoacoustic tomography with limited noisy data are iterative in nature to provide accurate solutions. These methods performance is highly affected by the noise level in the photoacoustic data. A singular value decomposition (SVD) based plug and play priors method for solving photoacoustic inverse problem was proposed in this work to provide robustness to noise in the data. The method was shown to be superior as compared to total variation regularization, basis pursuit deconvolution and Lanczos Tikhonov based regularization and provided improved performance in case of noisy data. The numerical and experimental cases show that the improvement can be as high as 8.1 dB in signal to noise ratio of the reconstructed image and 67.98% in root mean square error in comparison to the state of the art methods.

Data-specific mask-guided image reconstruction for diffuse optical tomography

Conventional approaches in diffuse optical tomography (DOT) image reconstruction often address the ill-posed inverse problem via regularization with a constant penalty parameter, which uniformly smooths out the solution. In this study, we present a data-specific mask-guided scheme that incorporates a prior mask constraint into the image reconstruction framework. The prior mask was created from the DOT data itself by exploiting the multi-measurement vector formulation. We accordingly propose two methods to integrate the prior mask into the reconstruction process. First, as a soft prior by exploiting a spatially varying regularization. Second, as a hard prior by imposing a region-of-interest-limited reconstruction. Furthermore, the latter method iterates between discrete and continuous steps to update the mask and optical parameters, respectively. The proposed methods showed enhanced optical contrast accuracy, improved spatial resolution, and reduced noise level in DOT reconstructed images compared with the conventional approaches such as the modified Levenberg-Marquardt approach and the l₁-regularization based sparse recovery approach.

Fractional Regularization to Improve Photoacoustic Tomographic Image Reconstruction

Photoacoustic tomography involves reconstructing the initial pressure rise distribution from the measured acoustic boundary data. The recovery of the initial pressure rise distribution tends to be an ill-posed problem in the presence of noise and when limited independent data is available, necessitating regularization. The standard regularization schemes include Tikhonov, l₁ -norm, and total-variation. These regularization schemes weigh the singular values equally irrespective of the noise level present in the data. This paper introduces a fractional framework to weigh the singular values with respect to a fractional power. This fractional framework was implemented for Tikhonov, l₁ -norm, and total-variation regularization schemes. Moreover, an automated method for choosing the fractional power was also proposed. It was shown theoretically and with numerical experiments that the fractional power is inversely related to the data noise level for fractional Tikhonov scheme. The fractional framework outperforms the standard regularization schemes, Tikhonov, l₁ -norm, and total-variation by 54% in numerical simulations, experimental phantoms, and in vivo rat data in terms of observed contrast/signal-to-noise-ratio of the reconstructed images.

Spatially variant regularization based on model resolution and fidelity embedding characteristics improves photoacoustic tomography

Photoacoustic tomography tends to be an ill-conditioned problem with noisy limited data requiring imposition of regularization constraints, such as standard Tikhonov (ST) or total variation (TV), to reconstruct meaningful initial pressure rise distribution from the tomographic acoustic measurements acquired at the boundary of the tissue. However, these regularization schemes do not account for nonuniform sensitivity arising due to limited detector placement at the boundary of tissue as well as other system parameters. For the first time, two regularization schemes were developed within the Tikhonov framework to address these issues in photoacoustic imaging. The model resolution, based on spatially varying regularization, and fidelity-embedded regularization, based on orthogonality between the columns of system matrix, were introduced. These were systematically evaluated with the help of numerical and in-vivo mice data. It was shown that the performance of the proposed spatially varying regularization schemes were superior (with at least 2 dB or 1.58 times improvement in the signal-to-noise ratio) compared to ST-/TV-based regularization schemes.

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

PURPOSE

Development of simple and computationally efficient extrapolated Tikhonov filtering reconstruction methods for photoacoustic tomography.

METHODS

The model-based reconstruction algorithms in photoacoustic tomography typically utilize Tikhonov regularization scheme for the reconstruction of initial pressure distribution from the measured boundary acoustic data. The automated choice of regularization parameter in these cases is computationally expensive. Moreover, the Tikhonov scheme promotes the smooth features in the reconstructed image due to the smooth regularizer, thus leading to loss of sharp features. The proposed extrapolation method estimates the solution at zero regularization assuming the solution being a function of regularization parameter and thus posing it as a zero value problem. Thus, the numerically computed zero regularization solution is expected to have better features compared to standard Tikhonov solution, with an added advantage of removing the necessity of automated choice of regularization. The reconstructed results using this method were shown in three variants (Lanczos, traditional, and exponential) of Tikhonov filtering and were compared with the standard error estimate technique.

RESULTS

Four numerical (including realistic breast phantom) and two experimental phantom data were utilized to show the effectiveness of the proposed method. It was shown that the proposed method performance was superior than the standard error estimate technique, being at least four times faster in terms of computation, and provides an improvement as high as 2.6 times in terms of standard figures of merit.

CONCLUSION

The developed extrapolated Tikhonov filtering methods overcome the difficulty of obtaining a suitable regularization parameter and shown to be reconstructing high-quality photoacoustic images with additional advantage of being computationally efficient, making it more appealing in real-time applications.

Computationally efficient error estimate for evaluation of regularization in photoacoustic tomography

The model-based image reconstruction techniques for photoacoustic (PA) tomography require an explicit regularization. An error estimate (?2) minimization-based approach was proposed and developed for the determination of a regularization parameter for PA imaging. The regularization was used within Lanczos bidiagonalization framework, which provides the advantage of dimensionality reduction for a large system of equations. It was shown that the proposed method is computationally faster than the state-of-the-art techniques and provides similar performance in terms of quantitative accuracy in reconstructed images. It was also shown that the error estimate (?2) can also be utilized in determining a suitable regularization parameter for other popular techniques such as Tikhonov, exponential, and nonsmooth (?1 and total variation norm based) regularization methods.