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Prostate cancer is the most common malignancy among men. To confirm an initial detection by a prostate-specific antigen test, magnetic resonance imaging (MRI) is used, but MRI is costly. Ultrasound is a costeffective imaging modality and shows promising results in diagnosing prostate cancer, especially the dynamic contrast-enhanced ultrasound. Dynamic contrast-enhanced ultrasound (DCEUS) is an imaging modality that allows the imaging of the injected microbubbles by exploiting their non-linear acoustic scatter. Because of their size, comparable to red blood cells, ultrasound contrast agents can flow through the vascular tree down to the microvessels, enabling the visualization and, possibly, quantification of the angiogenic processes associated with cancer growth. Although several techniques are applied to DCEUS to reduce noise, speckle noise still exists.
Speckle noise occurs due to the coherent imaging of many microbubbles in one resolution cell. In existing methods, a low-rank matrix decomposition is applied to the DCEUS acquisitions using singular value decomposition, and the despeckling is done by keeping the highest few singular vectors and values. The DCEUS acquisitions come in a tensor format, rich with higher-order structure. The application of the matrixbased denoising technique does not utilize the original tensor structure. This dissertation focuses on despeckling through higher-order tensor decomposition methods. We tackle the following research question: "How can low-rank tensor decomposition methods be leveraged to effectively denoise DCEUS acquisitions of the prostate for improved prostate cancer detection?" We apply tensor decomposition methods that utilize orthogonal factors. In the spatial domain, the orthogonality allows the separation of the malignant and benign regions and the separation of the tissue and the vasculature. In the time domain, the orthogonality allows for capturing the components that correspond with the bubble movement and rejects the components related to the noise.
Despeckling of DCEUS through low-rank tensor decomposition has not been conducted before, and we propose tensor estimation algorithms for this application by utilizing established tensor decomposition frameworks. We start our research by modeling speckle noise as white Gaussian noise (WGN) with sparse outliers. We assess the performance of convex tensor estimation algorithms through simulation. We propose a novel weighting scheme for the soft-thresholding of the singular values. Instead of iterative thresholding, we can truncate the tensor and deviispeckle the DCEUS acquisitions. We propose a rank estimation method for DCEUS acquisitions. Instead of modeling speckle noise as WGN with sparse outliers, we minimize its negative log-likelihood and propose a gradient-based denoising algorithm.
Next, we investigate the classification performance of prostate cancer by comparing the proposed algorithms with the literature. We use the area under the receiver-operator characteristic curve (ROC-AUC) metric to assess the classification performance. For the voxel-based cancer diagnosis of 94 prostate cancer patients, truncated multilinear singular value decomposition has a better performance for the majority of the prostate cancer markers when the ROC-AUC metric is used. A rank estimation technique incorporating WGN with sparse outliers, followed by truncated multilinear singular value decomposition (tr-MLSVD), is the best-performing denoising method for DCEUS. In the context of the main research question, the cancer diagnosis performance of DCEUS acquisitions improves the majority of the time when a tensor-based denoising technique is used. On average, the tensor-based denoising techniques yield approximately a 1.6% relative improvement in the ROC-AUC metric compared to the literature. This translates to billions of additional correct voxel-level malignancy discriminations in our clinical study, which may significantly impact downstream classification and localization performance.
We conclude with a theoretical study on the lower bound of the tensor decomposition method that performs the best for despeckling DCEUS. We calculate a lower bound for estimating the components of MLSVD when the ranks are known. In general, the CCRB that lower bounds the variance of the unbiased estimates of the components of MLSVD does not exist due to the non-uniqueness of the decomposition. However, when the mode-n singular values are unique, the CCRB exists. Additionally, when the multilinear ranks are high and modal singular values are well-separated, it is a tight bound. Such cases do not typically occur with real data such as DCEUS, highlighting the limited modeling capability of the CCRB.
...
Speckle noise occurs due to the coherent imaging of many microbubbles in one resolution cell. In existing methods, a low-rank matrix decomposition is applied to the DCEUS acquisitions using singular value decomposition, and the despeckling is done by keeping the highest few singular vectors and values. The DCEUS acquisitions come in a tensor format, rich with higher-order structure. The application of the matrixbased denoising technique does not utilize the original tensor structure. This dissertation focuses on despeckling through higher-order tensor decomposition methods. We tackle the following research question: "How can low-rank tensor decomposition methods be leveraged to effectively denoise DCEUS acquisitions of the prostate for improved prostate cancer detection?" We apply tensor decomposition methods that utilize orthogonal factors. In the spatial domain, the orthogonality allows the separation of the malignant and benign regions and the separation of the tissue and the vasculature. In the time domain, the orthogonality allows for capturing the components that correspond with the bubble movement and rejects the components related to the noise.
Despeckling of DCEUS through low-rank tensor decomposition has not been conducted before, and we propose tensor estimation algorithms for this application by utilizing established tensor decomposition frameworks. We start our research by modeling speckle noise as white Gaussian noise (WGN) with sparse outliers. We assess the performance of convex tensor estimation algorithms through simulation. We propose a novel weighting scheme for the soft-thresholding of the singular values. Instead of iterative thresholding, we can truncate the tensor and deviispeckle the DCEUS acquisitions. We propose a rank estimation method for DCEUS acquisitions. Instead of modeling speckle noise as WGN with sparse outliers, we minimize its negative log-likelihood and propose a gradient-based denoising algorithm.
Next, we investigate the classification performance of prostate cancer by comparing the proposed algorithms with the literature. We use the area under the receiver-operator characteristic curve (ROC-AUC) metric to assess the classification performance. For the voxel-based cancer diagnosis of 94 prostate cancer patients, truncated multilinear singular value decomposition has a better performance for the majority of the prostate cancer markers when the ROC-AUC metric is used. A rank estimation technique incorporating WGN with sparse outliers, followed by truncated multilinear singular value decomposition (tr-MLSVD), is the best-performing denoising method for DCEUS. In the context of the main research question, the cancer diagnosis performance of DCEUS acquisitions improves the majority of the time when a tensor-based denoising technique is used. On average, the tensor-based denoising techniques yield approximately a 1.6% relative improvement in the ROC-AUC metric compared to the literature. This translates to billions of additional correct voxel-level malignancy discriminations in our clinical study, which may significantly impact downstream classification and localization performance.
We conclude with a theoretical study on the lower bound of the tensor decomposition method that performs the best for despeckling DCEUS. We calculate a lower bound for estimating the components of MLSVD when the ranks are known. In general, the CCRB that lower bounds the variance of the unbiased estimates of the components of MLSVD does not exist due to the non-uniqueness of the decomposition. However, when the mode-n singular values are unique, the CCRB exists. Additionally, when the multilinear ranks are high and modal singular values are well-separated, it is a tight bound. Such cases do not typically occur with real data such as DCEUS, highlighting the limited modeling capability of the CCRB.
...
Prostate cancer is the most common malignancy among men. To confirm an initial detection by a prostate-specific antigen test, magnetic resonance imaging (MRI) is used, but MRI is costly. Ultrasound is a costeffective imaging modality and shows promising results in diagnosing prostate cancer, especially the dynamic contrast-enhanced ultrasound. Dynamic contrast-enhanced ultrasound (DCEUS) is an imaging modality that allows the imaging of the injected microbubbles by exploiting their non-linear acoustic scatter. Because of their size, comparable to red blood cells, ultrasound contrast agents can flow through the vascular tree down to the microvessels, enabling the visualization and, possibly, quantification of the angiogenic processes associated with cancer growth. Although several techniques are applied to DCEUS to reduce noise, speckle noise still exists.
Speckle noise occurs due to the coherent imaging of many microbubbles in one resolution cell. In existing methods, a low-rank matrix decomposition is applied to the DCEUS acquisitions using singular value decomposition, and the despeckling is done by keeping the highest few singular vectors and values. The DCEUS acquisitions come in a tensor format, rich with higher-order structure. The application of the matrixbased denoising technique does not utilize the original tensor structure. This dissertation focuses on despeckling through higher-order tensor decomposition methods. We tackle the following research question: "How can low-rank tensor decomposition methods be leveraged to effectively denoise DCEUS acquisitions of the prostate for improved prostate cancer detection?" We apply tensor decomposition methods that utilize orthogonal factors. In the spatial domain, the orthogonality allows the separation of the malignant and benign regions and the separation of the tissue and the vasculature. In the time domain, the orthogonality allows for capturing the components that correspond with the bubble movement and rejects the components related to the noise.
Despeckling of DCEUS through low-rank tensor decomposition has not been conducted before, and we propose tensor estimation algorithms for this application by utilizing established tensor decomposition frameworks. We start our research by modeling speckle noise as white Gaussian noise (WGN) with sparse outliers. We assess the performance of convex tensor estimation algorithms through simulation. We propose a novel weighting scheme for the soft-thresholding of the singular values. Instead of iterative thresholding, we can truncate the tensor and deviispeckle the DCEUS acquisitions. We propose a rank estimation method for DCEUS acquisitions. Instead of modeling speckle noise as WGN with sparse outliers, we minimize its negative log-likelihood and propose a gradient-based denoising algorithm.
Next, we investigate the classification performance of prostate cancer by comparing the proposed algorithms with the literature. We use the area under the receiver-operator characteristic curve (ROC-AUC) metric to assess the classification performance. For the voxel-based cancer diagnosis of 94 prostate cancer patients, truncated multilinear singular value decomposition has a better performance for the majority of the prostate cancer markers when the ROC-AUC metric is used. A rank estimation technique incorporating WGN with sparse outliers, followed by truncated multilinear singular value decomposition (tr-MLSVD), is the best-performing denoising method for DCEUS. In the context of the main research question, the cancer diagnosis performance of DCEUS acquisitions improves the majority of the time when a tensor-based denoising technique is used. On average, the tensor-based denoising techniques yield approximately a 1.6% relative improvement in the ROC-AUC metric compared to the literature. This translates to billions of additional correct voxel-level malignancy discriminations in our clinical study, which may significantly impact downstream classification and localization performance.
We conclude with a theoretical study on the lower bound of the tensor decomposition method that performs the best for despeckling DCEUS. We calculate a lower bound for estimating the components of MLSVD when the ranks are known. In general, the CCRB that lower bounds the variance of the unbiased estimates of the components of MLSVD does not exist due to the non-uniqueness of the decomposition. However, when the mode-n singular values are unique, the CCRB exists. Additionally, when the multilinear ranks are high and modal singular values are well-separated, it is a tight bound. Such cases do not typically occur with real data such as DCEUS, highlighting the limited modeling capability of the CCRB.
Speckle noise occurs due to the coherent imaging of many microbubbles in one resolution cell. In existing methods, a low-rank matrix decomposition is applied to the DCEUS acquisitions using singular value decomposition, and the despeckling is done by keeping the highest few singular vectors and values. The DCEUS acquisitions come in a tensor format, rich with higher-order structure. The application of the matrixbased denoising technique does not utilize the original tensor structure. This dissertation focuses on despeckling through higher-order tensor decomposition methods. We tackle the following research question: "How can low-rank tensor decomposition methods be leveraged to effectively denoise DCEUS acquisitions of the prostate for improved prostate cancer detection?" We apply tensor decomposition methods that utilize orthogonal factors. In the spatial domain, the orthogonality allows the separation of the malignant and benign regions and the separation of the tissue and the vasculature. In the time domain, the orthogonality allows for capturing the components that correspond with the bubble movement and rejects the components related to the noise.
Despeckling of DCEUS through low-rank tensor decomposition has not been conducted before, and we propose tensor estimation algorithms for this application by utilizing established tensor decomposition frameworks. We start our research by modeling speckle noise as white Gaussian noise (WGN) with sparse outliers. We assess the performance of convex tensor estimation algorithms through simulation. We propose a novel weighting scheme for the soft-thresholding of the singular values. Instead of iterative thresholding, we can truncate the tensor and deviispeckle the DCEUS acquisitions. We propose a rank estimation method for DCEUS acquisitions. Instead of modeling speckle noise as WGN with sparse outliers, we minimize its negative log-likelihood and propose a gradient-based denoising algorithm.
Next, we investigate the classification performance of prostate cancer by comparing the proposed algorithms with the literature. We use the area under the receiver-operator characteristic curve (ROC-AUC) metric to assess the classification performance. For the voxel-based cancer diagnosis of 94 prostate cancer patients, truncated multilinear singular value decomposition has a better performance for the majority of the prostate cancer markers when the ROC-AUC metric is used. A rank estimation technique incorporating WGN with sparse outliers, followed by truncated multilinear singular value decomposition (tr-MLSVD), is the best-performing denoising method for DCEUS. In the context of the main research question, the cancer diagnosis performance of DCEUS acquisitions improves the majority of the time when a tensor-based denoising technique is used. On average, the tensor-based denoising techniques yield approximately a 1.6% relative improvement in the ROC-AUC metric compared to the literature. This translates to billions of additional correct voxel-level malignancy discriminations in our clinical study, which may significantly impact downstream classification and localization performance.
We conclude with a theoretical study on the lower bound of the tensor decomposition method that performs the best for despeckling DCEUS. We calculate a lower bound for estimating the components of MLSVD when the ranks are known. In general, the CCRB that lower bounds the variance of the unbiased estimates of the components of MLSVD does not exist due to the non-uniqueness of the decomposition. However, when the mode-n singular values are unique, the CCRB exists. Additionally, when the multilinear ranks are high and modal singular values are well-separated, it is a tight bound. Such cases do not typically occur with real data such as DCEUS, highlighting the limited modeling capability of the CCRB.
Journal article
(2025)
-
Metin Calis, Massimo Mischi, Alle-Jan van der Veen, Raj Thilak Rajan, Borbàla Hunyadi
Tensor decomposition methods for signal processing applications are an active area of research. Real data are often low-rank, noisy, and come in a higher-order format. As such, low-rank tensor approximation methods that account for the high-order structure of the data are often used for denoising. One way to represent a tensor in a low-rank form is to decompose the tensor into a set of orthonormal factor matrices and an all-orthogonal core tensor using a higher-order singular value decomposition. Under noisy measurements, the lower bound for recovering the factor matrices and the core tensor is unknown. In this paper, we exploit the well-studied constrained Cramér-Rao bound to calculate a lower bound on the mean squared error of the unbiased estimates of the components of the multilinear singular value decomposition under additive white Gaussian noise, and we validate our approach through simulations.
...
Tensor decomposition methods for signal processing applications are an active area of research. Real data are often low-rank, noisy, and come in a higher-order format. As such, low-rank tensor approximation methods that account for the high-order structure of the data are often used for denoising. One way to represent a tensor in a low-rank form is to decompose the tensor into a set of orthonormal factor matrices and an all-orthogonal core tensor using a higher-order singular value decomposition. Under noisy measurements, the lower bound for recovering the factor matrices and the core tensor is unknown. In this paper, we exploit the well-studied constrained Cramér-Rao bound to calculate a lower bound on the mean squared error of the unbiased estimates of the components of the multilinear singular value decomposition under additive white Gaussian noise, and we validate our approach through simulations.
Dynamic contrast-enhanced ultrasound (DCEUS) is an imaging modality for assessing microvascular perfusion and dispersion kinetics. However, the presence of speckle noise may hamper the quantitative analysis of the contrast kinetics. Common speckle denoising techniques based on low-rank approximations typically model the speckle noise as white Gaussian noise (WGN) after the log transformation and apply matrix-based algorithms. We address the high dimensionality of the 4D DCEUS data and apply low-rank tensor decomposition techniques to denoise speckles. Although there are many tensor decompositions that can describe low rankness, we limit our research to multilinear rank and tubal rank. We introduce a gradient-based extension of the multilinear singular value decomposition to model low multilinear rankness, assuming that the log-transformed speckle noise follows a Fisher-tippet distribution. In addition, we apply an algorithm based on tensor singular value decomposition to model low tubal rankness, assuming that the log-transformed speckle noise is WGN with sparse outliers. The effectiveness of the methods is evaluated through simulations and phantom studies. Additionally, the tensor-based algorithms’ real-world performance is assessed using DCEUS prostate recordings. Comparative analyses with existing DCEUS denoising literature are conducted, and the algorithms’ capabilities are showcased in the context of prostate cancer classification. The addition of Fisher-tippet distribution did not improve the results of tr-MLSVD in the in vivo case. However, most cancer markers are better distinguishable when using a tensor denoising technique than state-of-the-art approaches.
...
Dynamic contrast-enhanced ultrasound (DCEUS) is an imaging modality for assessing microvascular perfusion and dispersion kinetics. However, the presence of speckle noise may hamper the quantitative analysis of the contrast kinetics. Common speckle denoising techniques based on low-rank approximations typically model the speckle noise as white Gaussian noise (WGN) after the log transformation and apply matrix-based algorithms. We address the high dimensionality of the 4D DCEUS data and apply low-rank tensor decomposition techniques to denoise speckles. Although there are many tensor decompositions that can describe low rankness, we limit our research to multilinear rank and tubal rank. We introduce a gradient-based extension of the multilinear singular value decomposition to model low multilinear rankness, assuming that the log-transformed speckle noise follows a Fisher-tippet distribution. In addition, we apply an algorithm based on tensor singular value decomposition to model low tubal rankness, assuming that the log-transformed speckle noise is WGN with sparse outliers. The effectiveness of the methods is evaluated through simulations and phantom studies. Additionally, the tensor-based algorithms’ real-world performance is assessed using DCEUS prostate recordings. Comparative analyses with existing DCEUS denoising literature are conducted, and the algorithms’ capabilities are showcased in the context of prostate cancer classification. The addition of Fisher-tippet distribution did not improve the results of tr-MLSVD in the in vivo case. However, most cancer markers are better distinguishable when using a tensor denoising technique than state-of-the-art approaches.
Speckle noise is commonly assumed to be multiplicative. Non-local speckle denoising algorithms stack the correlated data patches into a tensor and take the logarithm such that the noise becomes additive. The log-transformed speckle noise is commonly assumed to be white Gaussian noise. The denoising is done through the low-rank approximation techniques applied to the non-local data patches. However, the log-transformed speckle noise can be better approximated as white Gaussian noise with sparse outliers. In this paper, we model the log-transformed speckle noise with this assumption and assess the importance of the noise model under various SNRs. In addition, we propose a weighting scheme for the tensor-based low-rank convex denoising method that utilizes the known ranks. The performance of the proposed algorithm is benchmarked against truncated multilinear singular value decomposition, higher-order orthogonal iteration, and robust tensor decomposition methods that use the sum of the nuclear norm and the tubal nuclear norm. Robust tensor decomposition methods that use the tubal nuclear norm perform better in low SNR scenarios. For high SNR scenarios, the proposed algorithm is found to perform better.
...
Speckle noise is commonly assumed to be multiplicative. Non-local speckle denoising algorithms stack the correlated data patches into a tensor and take the logarithm such that the noise becomes additive. The log-transformed speckle noise is commonly assumed to be white Gaussian noise. The denoising is done through the low-rank approximation techniques applied to the non-local data patches. However, the log-transformed speckle noise can be better approximated as white Gaussian noise with sparse outliers. In this paper, we model the log-transformed speckle noise with this assumption and assess the importance of the noise model under various SNRs. In addition, we propose a weighting scheme for the tensor-based low-rank convex denoising method that utilizes the known ranks. The performance of the proposed algorithm is benchmarked against truncated multilinear singular value decomposition, higher-order orthogonal iteration, and robust tensor decomposition methods that use the sum of the nuclear norm and the tubal nuclear norm. Robust tensor decomposition methods that use the tubal nuclear norm perform better in low SNR scenarios. For high SNR scenarios, the proposed algorithm is found to perform better.
Many beam-forming algorithms available for hearing aids, preserve both the interaural time differences (ITDs) and the interaural level differences (ILDs) of the interferers. Constraining both the spatial cues over all frequencies will exhaust the degrees of freedom (DoF) available for noise reduction in the filter design. The binaural cues, however, are frequency selective, i.e., the ITDs are dominant in the frequency range below 1.5 kHz and the ILDs are dominant at frequencies above 1.5 kHz. Hence in this paper, we propose two methods to preserve only the ILDs of the interferers, in the higher frequencies, while keeping the target undistorted. Since these formulations are nonconvex, quadratically constrained quadratic programs (QCQPs), an approximate convex relaxation is proposed. The proposed methods preserve the ILDs in the higher frequencies while an available algorithm that preserves interaural transfer function (ITF) of the interferers is used for the lower frequencies. The performance of the methods proposed are evaluated through simulations and the localization performance is validated through informal listening tests.
...
Many beam-forming algorithms available for hearing aids, preserve both the interaural time differences (ITDs) and the interaural level differences (ILDs) of the interferers. Constraining both the spatial cues over all frequencies will exhaust the degrees of freedom (DoF) available for noise reduction in the filter design. The binaural cues, however, are frequency selective, i.e., the ITDs are dominant in the frequency range below 1.5 kHz and the ILDs are dominant at frequencies above 1.5 kHz. Hence in this paper, we propose two methods to preserve only the ILDs of the interferers, in the higher frequencies, while keeping the target undistorted. Since these formulations are nonconvex, quadratically constrained quadratic programs (QCQPs), an approximate convex relaxation is proposed. The proposed methods preserve the ILDs in the higher frequencies while an available algorithm that preserves interaural transfer function (ITF) of the interferers is used for the lower frequencies. The performance of the methods proposed are evaluated through simulations and the localization performance is validated through informal listening tests.
The processing of low-frequency interaural time differences is found to be problematic among hearing-impaired people. The current generation of beamformers does not consider this deficiency. In an attempt to tackle this issue, we propose to replace the inaudible interaural time differences in the low-frequency region with the interaural level differences. In addition, a beamformer is introduced and analyzed, which enhances the low-frequency interaural level differences of the sound sources using a near-field transformation. The proposed beamforming problem is relaxed to a convex problem using semi-definite relaxation. The instrumental analysis suggests that the low-frequency interaural level differences are enhanced without hindering the provided intelligibility. A psychoacoustic localization test is done using a listening experiment, which suggests that the replacement of time differences into level differences improves the localization performance of normal-hearing listeners for an anechoic scene but not for a reverberant scene.
...
The processing of low-frequency interaural time differences is found to be problematic among hearing-impaired people. The current generation of beamformers does not consider this deficiency. In an attempt to tackle this issue, we propose to replace the inaudible interaural time differences in the low-frequency region with the interaural level differences. In addition, a beamformer is introduced and analyzed, which enhances the low-frequency interaural level differences of the sound sources using a near-field transformation. The proposed beamforming problem is relaxed to a convex problem using semi-definite relaxation. The instrumental analysis suggests that the low-frequency interaural level differences are enhanced without hindering the provided intelligibility. A psychoacoustic localization test is done using a listening experiment, which suggests that the replacement of time differences into level differences improves the localization performance of normal-hearing listeners for an anechoic scene but not for a reverberant scene.
Average consensus algorithms are used in many distributed systems such as distributed optimization, sensor fusion and the control of dynamic systems. Consensus algorithms converge through an explicit exchange of state variables. In some cases, however, the state variables are confidential. In this paper, a privacy-preserving asynchronous distributed average consensus method is proposed, which decomposes the initial values into two states; alpha states and beta states. These states are initialized such that their sum is twice the initial value. The alpha states are used to communicate with the other nodes, while the beta states are used internally. Although beta states are not shared, they are used in the update of the alpha states. Unlike differential privacy based methods, the proposed algorithm achieves the exact average consensus, while providing privacy to the initial values. Compared to the synchronous state decomposition algorithm, the convergence rate is improved without any privacy compromise. As the variances of coupling weights become infinitely large, the semi-honest adversary does not have any range to estimate the initial value of the nodes given that there is at least one coupling weight hidden from the adversary.
...
Average consensus algorithms are used in many distributed systems such as distributed optimization, sensor fusion and the control of dynamic systems. Consensus algorithms converge through an explicit exchange of state variables. In some cases, however, the state variables are confidential. In this paper, a privacy-preserving asynchronous distributed average consensus method is proposed, which decomposes the initial values into two states; alpha states and beta states. These states are initialized such that their sum is twice the initial value. The alpha states are used to communicate with the other nodes, while the beta states are used internally. Although beta states are not shared, they are used in the update of the alpha states. Unlike differential privacy based methods, the proposed algorithm achieves the exact average consensus, while providing privacy to the initial values. Compared to the synchronous state decomposition algorithm, the convergence rate is improved without any privacy compromise. As the variances of coupling weights become infinitely large, the semi-honest adversary does not have any range to estimate the initial value of the nodes given that there is at least one coupling weight hidden from the adversary.