Exponential filtering of singular values improves photoacoustic image reconstruction

Bhatt, Manish; Gutta, Sreedevi; Yalavarthy, Phaneendra K.

doi:10.1364/josaa.33.001785

Cited by 14 publications

(29 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…resulting in,13,17

x_{Tik} = {(A^{T} A + λ L^{T} L)}^{- 1} A^{T} b .

The properties of the solution depend on the choice of the regularization ( L and λ ). The standard (zeroth order) choice for L is identity matrix ( I ); thus, the solution becomes

x_{Tik} = {(A^{T} A + λ I)}^{- 1} A^{T} b .

These regularization methods involve matrix–matrix multiplications as well as solving large system of equations, which is computationally expensive. Therefore, the Tikhonov regularization was implemented in a Lanczos bidiagonalization framework, to reduce the computational complexity .…”

Section: Model‐based Reconstruction Algorithmsmentioning

confidence: 99%

“…The solution given in Eq. can be rewritten using the SVD of A as

x_{Tik} = V S^{†} U^{T} b,

where

S^{†} = d i a g (\frac{F_{i}}{S_{i}}),

with the filter factors F i being

F_{i} = \frac{S_{i}^{2}}{S_{i}^{2} + λ} .

Therefore, the Tikhonov solution with the filter factors become

x_{Tik} = {false\sum}_{i = 1}^{k} \frac{S_{i}^{2}}{S_{i}^{2} + λ} \frac{< U_{i}, b >}{S_{i}} V_{i},

where k = min ( m , n 2 ) with < .,. > representing the inner product operation of the argument vectors.…”

Section: Model‐based Reconstruction Algorithmsmentioning

confidence: 99%

“…The filter factors [in Eq. ] for exponential filtering are given as

F_{i} = 1 - e x p (\frac{- S_{i}^{2}}{λ}) .

The regularized exponential filtering solution using the filter factors thus become

x_{Exp} = {false\sum}_{i = 1}^{k} 2.047em2.047emtrue[1 - e x p (\frac{- S_{i}^{2}}{λ}) 2.047em2.047emtrue] \frac{< U_{i}, b >}{S_{i}} V_{i} .

The exponential filtering and Tikhonov filter factors become equal when

S_{i}^{2} < < λ

, logically making exponential filtering perform as an asymptotic regularization. The spectral filtering methods discussed so far, Tikhonov and exponential filtering has a major limitation in terms of computation of SVD of system matrix, which is of

O (m * n^{4})

complexity, but the decomposition can be performed a‐priori and can be seen as a one‐time overhead for a fixed data collection geometry.…”

Section: Model‐based Reconstruction Algorithmsmentioning

confidence: 99%

See 2 more Smart Citations

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…resulting in,13,17

x_{Tik} = {(A^{T} A + λ L^{T} L)}^{- 1} A^{T} b .

The properties of the solution depend on the choice of the regularization ( L and λ ). The standard (zeroth order) choice for L is identity matrix ( I ); thus, the solution becomes

x_{Tik} = {(A^{T} A + λ I)}^{- 1} A^{T} b .

Section: Model‐based Reconstruction Algorithmsmentioning

confidence: 99%

“…The solution given in Eq. can be rewritten using the SVD of A as

x_{Tik} = V S^{†} U^{T} b,

where

S^{†} = d i a g (\frac{F_{i}}{S_{i}}),

with the filter factors F i being

F_{i} = \frac{S_{i}^{2}}{S_{i}^{2} + λ} .

Therefore, the Tikhonov solution with the filter factors become

x_{Tik} = {false\sum}_{i = 1}^{k} \frac{S_{i}^{2}}{S_{i}^{2} + λ} \frac{< U_{i}, b >}{S_{i}} V_{i},

where k = min ( m , n 2 ) with < .,. > representing the inner product operation of the argument vectors.…”

Section: Model‐based Reconstruction Algorithmsmentioning

confidence: 99%

“…The filter factors [in Eq. ] for exponential filtering are given as

F_{i} = 1 - e x p (\frac{- S_{i}^{2}}{λ}) .

The regularized exponential filtering solution using the filter factors thus become

x_{Exp} = {false\sum}_{i = 1}^{k} 2.047em2.047emtrue[1 - e x p (\frac{- S_{i}^{2}}{λ}) 2.047em2.047emtrue] \frac{< U_{i}, b >}{S_{i}} V_{i} .

The exponential filtering and Tikhonov filter factors become equal when

S_{i}^{2} < < λ

O (m * n^{4})

complexity, but the decomposition can be performed a‐priori and can be seen as a one‐time overhead for a fixed data collection geometry.…”

Section: Model‐based Reconstruction Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…3,4 Inversion in limited data scenarios is difficult due to the ill-conditioned nature of the problem. 4,5 Therefore typically, prior statistics about the image is applied in the form of regularization during the inversion. 4,6 Another perspective of regularization lies in its ability to define resolution characteristics in the imaging domain.…”

mentioning

confidence: 99%

“…9 The second regularization scheme is based on model-resolution matrix, which provides the spatially variant characteristics of the model, that is proven to provide superior results compared to other regularization schemes in diffuse optical tomography. 8 The performance of the regularization schemes are compared with ST- 5 and total variation (TV) 10 -based schemes using numerical simulations and in-vivo experimental data.…”

mentioning

confidence: 99%

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

Sanny¹,

Prakash²,

Kalva

et al. 2018

J. Biomed. Opt.

View full text Add to dashboard Cite

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 fidelityembedded 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. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

show abstract

Regularized minimal residual method for permittivity reconstruction in microwave imaging

Magdum

Erramshetty

Jagannath

2020

Micro & Optical Tech Letters

View full text Add to dashboard Cite

In this paper, a regularized reconstruction based on the minimal residual method is proposed for microwave imaging applications. The method provides optimum regularization parameter to estimate the distribution of permittivity values of unknown scatterers under test. Initially, the method is applied to Born approximated linear model for weak scatterers. The performance of this approach is compared with the commonly adopted Morozov's discrepancy principle used in conjunction with the Tikhonov regularization. The effectiveness of the method is assisted by simulating the various numerical examples of synthetic and experimental data. The results of numerical simulations validate that the proposed method is highly effective. Thereafter, a non‐linear inverse problem based on the inexact Newton method is examined for the estimation of strong scatterers. Here also, the proposed method is found to be helpful in terms of improving the image accuracy.

show abstract

Exponential filtering of singular values improves photoacoustic image reconstruction

Cited by 14 publications

References 35 publications

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

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

Regularized minimal residual method for permittivity reconstruction in microwave imaging

Contact Info

Product

Resources

About