Photoacoustic image reconstruction in an attenuating medium using singular-value decomposition

Photoacoustic (PA) imaging is an emerging imaging technique for many clinical applications. One of the challenges posed by clinical translation is that imaging systems often rely on a finite-aperture transducer rather than a full tomography system. This results in imaging artifacts arising from an underdetermined reconstruction of the initial pressure distribution (IPD). Furthermore, clinical applications often require deep imaging, resulting in a low-signal-to-noise ratio for the acquired signal because of strong light attenuation in tissue. Conventional approaches to reconstruct the IPD, such as back projection and time-reversal, do not adequately suppress the artifacts and noise. We propose a sparsity-based optimization approach that improves the reconstruction of IPD in PA imaging with a linear array ultrasound transducer. In simulation studies, the forward model matrix was measured from k-Wave simulations, and the approach was applied to reconstruct simulated point objects and the Shepp-Logan phantom. The results were compared with the conventional back projection, time-reversal approach, frequency-domain reconstruction, and the iterative least-squares approaches. In experimental studies, the forward model of our imaging system is directly measured by scanning a graphite point source through the imaging field of view. Experimental images of graphite inclusions in tissue-mimicking phantoms are reconstructed and compared with the back projection and iterative least-squares approaches. Overall these results show that our proposed optimization approach can leverage the sparsity of the PA images to improve the reconstruction of the IPD and outperform the existing popular reconstruction approaches.

S-Wave Accelerates Optimization-based Photoacoustic Image Reconstruction in vivo

.Significance: Photoacoustic (PA) imaging can provide structural, functional, and molecular information for preclinical and clinical studies. For PA imaging (PAI), non-ideal signal detection deteriorates image quality, and quantitative PAI (QPAI) remains challenging due to the unknown light fluence spectra in deep tissue. In recent years, deep learning (DL) has shown outstanding performance when implemented in PAI, with applications in image reconstruction, quantification, and understanding.Aim: We provide (i) a comprehensive overview of the DL techniques that have been applied in PAI, (ii) references for designing DL models for various PAI tasks, and (iii) a summary of the future challenges and opportunities.Approach: Papers published before November 2020 in the area of applying DL in PAI were reviewed. We categorized them into three types: image understanding, reconstruction of the initial pressure distribution, and QPAI.Results: When applied in PAI, DL can effectively process images, improve reconstruction quality, fuse information, and assist quantitative analysis.Conclusion: DL has become a powerful tool in PAI. With the development of DL theory and technology, it will continue to boost the performance and facilitate the clinical translation of PAI.

Photoacoustic imaging with planar sensor arrays suffers from a finite aperture or limited view problem due to the fact that the sensor array is finite in size, whereas exact reconstruction algorithms require that it occupies the entire infinite plane. Here, acoustic reflectors are proposed as a means of reflecting the acoustic waves, that would otherwise not be measured, back onto the sensor, and it is shown that an existing FFT-based image reconstruction algorithm can be used to reconstruct an image in this case without modification. A 2D simulation is used to show the improvement in the image quality when data from the reverberant field is included in the reconstruction. The improvement is explained by the matching of the periodicity implicitly assumed by the FFT algorithm and the periodicity in the virtual initial pressure distribution formed from the real initial pressure distribution and an infinite line of image sources generated by the acoustic reflectors.

This paper concerns accurate computation of the singular value decomposition (SVD) of an $m\times n$ matrix $A$ . As is well known, cross-product matrix based SVD algorithms compute large singular values accurately but generally deliver poor small singular values. A new novel cross-product matrix based SVD method is proposed: (a) Use a backward stable algorithm to compute the eigenpairs of $A^{\rm T}A$ and take the square roots of the large eigenvalues of it as the large singular values of $A$ ; (b) form the Rayleigh quotient of $A^{\rm T}A$ with respect to the matrix consisting of the computed eigenvectors associated with the computed small eigenvalues of $A^{\rm T}A$ ; (c) compute the eigenvalues of the Rayleigh quotient and take the square roots of them as the small singular values of $A$ . A detailed quantitative error analysis is conducted on the method. It is proved that if small singular values are well separated from the large ones then the method can compute the small ones accurately up to the order of the unit roundoff $\epsilon$ . An algorithm is developed that is not only cheaper than the standard Golub–Reinsch and Chan SVD algorithms but also can update or downdate a new SVD by adding or deleting a row and compute certain refined Ritz vectors for large matrix eigenproblems at very low cost. Several variants of the algorithm are proposed that compute some or all parts of the SVD. Typical numerical examples confirm the high accuracy of our algorithm.

1 - Implicitly restarted arnoldi/lanczos methods and large scale svd applications

The Gram‐Charlier series was suggested as an empirical instrument spreading function in the first paper (part I) of this series. In the second paper (part II) of this series, the Fourier transform method was used together with the suggested series to solve Tung's integral equation. In this paper, an alternate method for solving Tung's equation is proposed which eliminates some of the limitations of the Fourier transform method. In the approach used in this study, Tung's integral equation is approximated by a set of linear equations. Since no unique least‐squares solution can be computed, a closely related problem whose solution closely approximates the original problem is formulated and solved using singular value decomposition. By avoiding the use of the smallest singular values and forcing the equality of the areas of the corrected and the uncorrected chromatograms, an approximate solution to the original problem is obtained in which the oscillations inherently present due to the ill‐posed nature of the problem are filtered out. The performance of the method with the experimental data given in Part II is indicated.

Multiple irradiation sensing of the optical effective attenuation coefficient for spectral correction in handheld OA imaging

Image enhancement and reconstruction is an important field of research in digital image analysis. To increase the quality of low-contrast images, a variety of image-enhancing technologies are available. Among these image enhancement techniques, singular value decomposition and discrete wavelet transform are the popular approaches for enhancing low-quality images. In this study, we have developed a modified singular value decomposition approach to enhance low-contrast and low-resolution close-circuit television images. Low-quality and low-resolution images with singular values near zero are used as input in the proposed approach. On the selected data, a threshold value was determined in the singular values of the diagonal matrix. Finally, the proposed modified singular value decomposition technique was applied to enhance the value of images with low quality and resolution. The datasets include 90 facial images of different individuals with low quality and resolution from a university database. The performance of the proposed approach is assessed using image entropy, peak signal to noise ratio, mean square error, contrast measurement and time computation. During the experiments performed on the obtained dataset, it was found that the proposed modified singular value decomposition approach outperformed the existing singular value decomposition, discrete wavelet transform-singular value decomposition and stationary wavelet transform methods.

In conventional biomedical photoacoustic tomography (PAT), ultrasonic pulses generated through the absorption of nanosecond pulses of near-infrared light are recorded over an array of detectors and used to recover an image of the initial acoustic pressure distribution within soft tissue. This image is related to the tissue optical coefficients and therefore carries information about the tissue physiology. For high resolution imaging, a large-area detector array with a high density of small, sensitive elements is required. Such arrays can be expensive, so reverberant-field PAT has been suggested as a means of obtaining PAT images using arrays with a smaller number of detectors. By recording the reflections from an acoustically reverberant cavity surrounding the sample, in addition to the primary acoustic pulse, sufficient information may be captured to allow an image to be reconstructed without the need for a large-area array. An initial study using two-dimensional simulations was performed to assess the feasibility of using a single detector for PAT. It is shown that reverberant-field data recorded at a single detector are sufficient to reconstruct the initial pressure distribution accurately, so long as the shape of the reverberant cavity makes it ray-chaotic. The practicalities of such an approach to photoacoustic imaging are discussed.

We consider the use of conjugate-gradient-like iterative methods for the solution of integral equations arising from an inverse problem in acoustics in a bounded three dimensional region. The inverse problem is the computation of the normal velocities on the boundary of a region from pressure measurements on an interior surface. The pressure satisfies the Helmholtz equation in the region. Two formulations are considered: one based on the representation of pressures by a single layer potential and the other based on the Helmholtz-Kirchhoff integral equation. Both formulations can be used to approximate the Neumann Green’s function as an alternative. The integral equations are all ill-posed and are discretized by a boundary element method. The resulting liner systems are ill-conditoned and a (smooth) regularized solutions must be sought. Two regularization rules, including a new one, for conjugate-gradient-like methods are applied and found to have advantages over a standard method based on the truncated singular value decomposition using generalized cross validation. Due to the occurence of multiple singular values for our integral operators, conjugate gradient methods compute the optimal solution in the first few iterations and prove to be particularly fast for these large scale acoustics problems.

Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored, including factorization methods. Factorization methods approximate the weight matrix of a DNN layer with the multiplication of two or multiple low-rank matrices. However, it is hard to measure the ranks of DNN layers during the training process. Previous works mainly induce low-rank through implicit approximations or via costly singular value decomposition (SVD) process on every training step. The former approach usually induces a high accuracy loss while the latter has a low efficiency. In this work, we propose SVD training, the first method to explicitly achieve low-rank DNNs during training without applying SVD on every step. SVD training first decomposes each layer into the form of its full-rank SVD, then performs training directly on the decomposed weights. We add orthogonality regularization to the singular vectors, which ensure the valid form of SVD and avoid gradient vanishing/exploding. Low-rank is encouraged by applying sparsity-inducing regularizers on the singular values of each layer. Singular value pruning is applied at the end to explicitly reach a low-rank model. We empirically show that SVD training can significantly reduce the rank of DNN layers and achieve higher reduction on computation load under the same accuracy, comparing to not only previous factorization methods but also state-of-the-art filter pruning methods.

Matrix factorization plays an important role in scientific computation. The widely used one is singular value decomposition (SVD) which approximates the original data matrix with three lower rank matrices with orthogonality constraints. Recently nonnegative matrix factorization (NMF) considering the nonnegativity of data makes the results more interpretable than those of SVD. However NMF finds only two factor matrices and there is no significant index as singular values of SVD which can be used for sorting learned basis vectors. In this paper we take into account the nonnegativity for SVD and propose nonnegative SVD (NNSVD). The preliminary results on the microarray data of spermatogenesis show that NNSVD has advantages of both SVD and NMF.

We monitored the occupancy of a functionally important non-coordinated water molecule in the distal heme pocket of sperm whale myoglobin over the pH range 4.3-9.4. Water occupancy was assessed by using time-resolved spectroscopy to detect the perturbation of the heme visible band absorption spectrum caused by water entry after CO photodissociation ( Goldbeck, R. A., Bhaskaran, S., Ortega, C., Mendoza, J. L., Olson, J. S., Soman, J., Kliger, D. S., and Esquerra, R. M. (2006) Proc. Natl. Acad. Sci. U. S. A. 103, 1254-1259 ). We found that the water occupancy observed during the time interval between ligand photolysis and diffusive recombination decreased by nearly 20% as the pH was lowered below 6. This decrease accounted for most of the concomitant increase in the observed CO bimolecular recombination rate constant, as the lower water occupancy presented a smaller kinetic barrier to CO entry into the pocket at lower pH. These results were consistent with a model in which the distal histidine, which stabilizes the water molecule within the distal pocket by accepting a hydrogen bond, tends to swing out of the pocket upon protonation and destabilize the water occupancy at low pH. Extrapolation of this model to lower pH suggests that the additional increase in ligand association rate constant observed previously in stopped-flow studies at pH 3 may also be due in part to reduced distal water occupancy concomitant with further His64 protonation and coupled protein conformational change.

In biomedical photoacoustic tomography (PAT), ultrasonic pulses generated by the absorption of near-infrared light are recorded over an array of detectors, and the measured pressure time series are used to recover an image of the initial acoustic pressure distribution within the tissue, which is related to the tissue optical coefficients and therefore to tissue physiology. For high resolution imaging, large-area detector arrays with a high density of sensitive, small elements are required. Such arrays can be expensive, so reverberant-field PAT has been suggested as a means of obtaining PAT images using arrays with a smaller number of detectors or even a single detector. We propose that by recording the reflections from a reverberant cavity in addition to the primary acoustic waves, sufficient information can be captured to allow a PAT image to be reconstructed, without the requirement for a large-area array. A pilot study using simple 2D simulations, backprojections and modal inversions was undertaken to assess the feasibility of this approach to PAT.