PaperlayerView exact revision on arXiv

Source-linked AI summary

Deep Unfolded Robust PCA with Application to Clutter Suppression in Ultrasound

Oren Solomon, Regev Cohen, Yi Zhang, Yi Yang, He Qiong, Jianwen Luo, Ruud J. G. van Sloun, Yonina C. Eldar

arXiv:1811.08252v1cs.LGeess.SPstat.ML

TL;DR

The paper addresses clutter suppression in contrast-enhanced ultrasound, where tissue and microbubble signals must be separated for vascular imaging. It models the data as low-rank tissue plus sparse contrast-agent components, solves the resulting robust PCA problem iteratively, and unfolds it into the CORONA network. Across simulations and in-vivo rat-brain scans, CORONA reports improved image quality and contrast, with faster and more accurate convergence than its iterative counterpart.

  • Problem

    Separating sparse microbubble signals from cluttering tissue signals is a crucial preprocessing challenge in contrast-enhanced ultrasound, while SVD filtering requires an uncertain discrimination threshold.

  • Method

    The paper uses a low-rank-plus-sparse robust PCA model with iterative principal component pursuit, then unfolds it into the convolutional CORONA network trained on simulated and in-vivo separated signals.

  • Results

    CORONA outperforms SVD, iterative RPCA, ResNet, and FISTA in reported image quality and contrast, while simulations show one CORONA layer achieves an order-of-magnitude-better MSE than 50 FISTA iterations.

  • Takeaways & Limitations

    The proposed model-based deep network improves vascular depiction in simulated and in-vivo rat-brain datasets while avoiding a-priori rank estimation.

  • Takeaways & Limitations

    Rank-dependent pursuit architectures require retraining for each new rank choice, limiting applicability when rank varies across applications or realizations.

Abstract

from arXiv · show

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented subwavelength spatial resolution by relying on super-resolution techniques. A typical preprocessing step in super-resolution ultrasound is to separate the microbubble signal from the cluttering tissue signal. This step has a crucial impact on the final image quality. Here, we propose a new approach to clutter removal based on robust principle component analysis (PCA) and deep learning. We begin by modeling the acquired contrast enhanced ultrasound signal as a combination of a low rank and sparse components. This model is used in robust PCA and was previously suggested in the context of ultrasound Doppler processing and dynamic magnetic resonance imaging. We then illustrate that an iterative algorithm based on this model exhibits improved separation of microbubble signal from the tissue signal over commonly practiced methods. Next, we apply the concept of deep unfolding to suggest a deep network architecture tailored to our clutter filtering problem which exhibits improved convergence speed and accuracy with respect to its iterative counterpart. We compare the performance of the suggested deep network on both simulations and in-vivo rat brain scans, with a commonly practiced deep-network architecture and the fast iterative shrinkage algorithm, and show that our architecture exhibits better image quality and contrast.

I. INTRODUCTION

CEUS clutter suppression must separate sparse contrast-agent signals from coherent tissue signals, but existing temporal, harmonic, and SVD-based methods have important limitations. The paper proposes robust PCA and its deep-unfolded CORONA network to improve separation, convergence, image quality, and contrast.

  • CEUS uses intravenously administered gas microbubbles to visualize vascular structures and support applications including capillary perfusion and sub-wavelength vascular imaging.
  • Temporal FIR/IIR filtering can require high filter order, long settling time, or fewer temporal samples, while harmonic imaging reduces frame rate and may leave nonlinear tissue signals.
  • SVD-based clutter filtering exploits tissue’s spatial coherence but is weakened by limited temporal and spatial samples and uncertainty in selecting a tissue-versus-blood singular-value threshold.
  • The proposed model decomposes beamformed ultrasound movies into a low-rank tissue matrix and sparse contrast-agent outliers, then retrieves the contrast signal through convex principal component pursuit.
  • CORONA unfolds the iterative algorithm into a fixed-length convolutional network, using convolutional layers and hybrid simulated/in-vivo training to improve convergence and reconstruction quality.
  • The paper compares CORONA with SVD, iterative RPCA, ResNet, and related iterative approaches, reporting better image quality and contrast across simulated and in-vivo rat-brain data.

A. Problem formulation

The acquired ultrasound movie is modeled as low-rank tissue, sparse contrast-agent signal, and noise, then separated by an iterative convex optimization procedure. This formulation exploits tissue’s spatiotemporal coherence and the sparse, spatially persistent distribution of contrast signals.

  • Signal model: Beamformed ultrasound frames are stacked into a measurement matrix D whose components represent tissue, contrast-agent signal, and additive noise.Each frame is vectorized before being placed as a column in D.
  • Signal model: The tissue matrix L is assumed low rank because tissue exhibits high spatiotemporal coherence, while the contrast matrix S is sparse because vessels sparsely populate the imaged medium.The matrices have size M^2 × T when each frame contains M × M pixels.
  • Convex formulation: The separation problem uses nuclear-norm regularization for L and a mixed l1,2 norm for S, reflecting low rank and spatially persistent vessel locations.The mixed norm aggregates row-wise l2 norms because the sparse pattern is shared across frames.
  • Iterative solution: ISTA solves the regularized least-squares problem through proximal updates using singular-value thresholding for L and mixed l1,2 soft thresholding for S.The iterative algorithm requires measurement matrices H1 and H2 and selected regularization parameters.
  • Iterative solution: As tissue-to-contrast dynamic range increases from 10dB to 60dB, more iterations are required, motivating a fixed-complexity unfolded algorithm.The stated dynamic-range observation directly motivates the subsequent CORONA design.

B. Unfolding the iterative algorithm

CORONA unfolds the low-rank-plus-sparse iterative solver into a convolutional feedforward network. Its learned convolution kernels and layer-specific thresholds replace model-dependent operations while retaining the iterative architecture.

  • Network construction: The kth iterative step is treated as the kth network layer, converting the recurrent optimization procedure into a feedforward architecture.The unfolded network is derived directly from the L+S ISTA updates.
  • Network construction: CORONA replaces matrices depending on H1 and H2 with learned two-dimensional convolution kernels.The convolution operator is applied within each unfolded layer.
  • Architectural design: Convolutional kernels provide spatial invariance while substantially reducing learned parameters relative to fully connected layers.This contrasts the implementation with previous unfolded RPCA work using fully connected layers.
  • Architectural design: The network treats recovered movies as three-dimensional volumes, applies 2D convolutions, and performs singular-value thresholding after reshaping the volume into a matrix.Thresholding coefficients are learned independently for each layer.
  • Architectural design: CORONA learns regularization and thresholding parameters during training rather than requiring them to be selected manually.The layer-specific thresholding values apply to both SVT and soft-thresholding operations.

C. Training CORONA

CORONA is trained supervisedly on examples pairing measurement data with sparse and low-rank decompositions. The training strategy combines patch-based processing, simulations, and in-vivo data to address limited organ-specific scan availability.

  • Supervised training: Supervised training pairs each measurement Di with corresponding sparse and low-rank targets, using a loss that sums MSEs for both outputs.Targets may come from simulations or iterative decompositions such as FISTA.
  • Supervised training: CORONA’s learnable parameters include convolution kernels and layer-specific regularization parameters across K unfolded layers.The sparse and low-rank outputs are trained jointly through these parameters.
  • Data preparation: Training uses 3D patches rather than entire ultrasound scans, and Algorithm 1 is applied independently to each training patch.Patch-based analysis reduces the practical burden of training on full scans.
  • Data preparation: The simulations model individual UCAs, their propagation, and cluttering tissue signals for generating training data.The paper also examines the importance of combining simulated and in-vivo data.

III. EXPERIMENTS

Experiments evaluate CORONA against ResNet and FISTA using simulated and in-vivo ultrasound data. The reported comparisons focus on image quality, contrast, and MSE convergence as the number of layers or iterations changes.

  • Experimental data: In-vivo experiments used two rat brains scanned with a 15MHz probe, acquiring over 6000 frames per rat and processing 300 selected frames.The scans used a 6×2mm2 craniotomy window and intravenously administered SonoVue contrast agent.
  • Baselines: ResNet was implemented with complex convolutions to recover only the UCA signal, whereas CORONA recovers both UCA and tissue signals.The comparison assesses the architectural differences for tissue-clutter suppression.
  • Results: CORONA outperforms ResNet in CEUS image quality, measured by contrast, according to the in-vivo comparison.The paper describes contrast as the image-quality criterion for this comparison.

A. Simulation results

Simulation experiments show that CORONA reliably recovers both UCA and tissue signals, while achieving substantially faster and more accurate convergence than FISTA.

  • CORONA reliably recovers both the simulated UCA signal and the low-rank tissue signal.The recovered UCA image provides a clearer depiction of the simulated vascular structure than ResNet.
  • ResNet qualitatively recovers the UCA signal, but with lower contrast than CORONA and incomplete recovery of the signal.The simulation comparison evaluates recovered UCA and tissue components against ground-truth images.
  • CORONA achieves an order-of-magnitude lower MSE with one layer than FISTA with 50 iterations.Adding layers improves CORONA initially, with performance remaining roughly unchanged after five layers.
  • FISTA’s MSE decreases with iteration, but requires dramatically more iterations to reach CORONA’s MSE values.Each CORONA layer corresponds conceptually to an iteration of the unfolded algorithm.

B. In-vivo experiments

In-vivo rat-brain experiments compare CORONA with SVD, FISTA, wall filtering, and ResNet using visual, profile, CNR, and CR evaluations. CORONA and the other deep-learning approaches provide less noisy, higher-contrast separation than conventional filtering, with CORONA generally achieving the strongest metrics.

  • Increasing the wall-filter cutoff from 0.2π to 0.9π suppresses more slow tissue but also removes slower bubbles, producing a less consistent vascular image.The cutoff choices represent a trade-off between tissue suppression and preservation of slow-moving UCAs.
  • CORONA, FISTA, and ResNet produce less noisy CEUS separation than SVD and wall filtering in rat-brain scans.The comparison includes wall-filter cutoffs of 0.2π and 0.9π, with color intensity reported in dB.
  • CNR and CR quantify contrast using selected signal patches relative to dashed-yellow background patches, with higher values indicating better contrast and noise suppression.The reported tables provide CNR and CR values for the selected green and red regions in Fig. 4.
  • CORONA outperforms all other approaches in CNR and CR across the reported in-vivo comparisons.In most cases, CORONA’s performance is an order of magnitude better than SVD; ResNet’s CR is better than SVD but its CNR is not always higher.
  • FISTA and the deep networks show higher-contrast intensity profiles than SVD and wall filtering, while all methods reconstruct the main peaks with good correspondence.Missing CORONA profile regions represent −∞ values, and all profile values are reported in dB.

V. DISCUSSION AND CONCLUSIONS

The paper’s low-rank-plus-sparse model exploits spatiotemporal structure and UCA sparsity, while CORONA unfolds the iterative solver into a convolutional deep network. CORONA improves reconstruction quality and vascular depiction, but trades lower parameter count and learned rank selection against slower training and execution.

  • Model and iterative separation: The proposed low-rank-plus-sparse model exploits spatiotemporal relations and UCA sparsity for tissue/UCA separation, outperforming commonly practiced SVD filtering.The model is solved with an iterative principal component pursuit algorithm.
  • Deep unfolding: CORONA unfolds the iterative algorithm into a deep network to improve execution time and reconstructed image quality.Its architecture uses convolution layers and a hybrid simulation-in-vivo training policy.
  • Training design: Training on patches reduces potential bias toward vessel trees in the relatively small training cohort compared with training on entire images.Small patches are less likely to include meaningful vessel structure.
  • Rank selection: The proposed convex formulation avoids manually estimating the low-rank degree q and trains against optimal RPCA reconstructions.Earlier factorized approaches require choosing q, which can vary across applications or realizations and require retraining.
  • CORONA–ResNet trade-off: CORONA uses 314 parameters for one layer and 1796 for ten layers, versus 25378 for ResNet, while outperforming ResNet in visual quality and quantifiable metrics.The trade-off is slower training and execution because CORONA performs SVD decomposition in each layer.
  • Scope and extension: The methods were demonstrated on CEUS IQ movies and could in principle extend to dynamic MRI and blood-tissue separation for Doppler processing.For blood-tissue separation, the larger dynamic range would require more iterations, after which the learned version could be trained for faster execution.

supporting materials

The supporting materials explain how learned unfolding replaces ISTA iterations with trainable layers and evaluate CORONA against ResNet and iterative methods under simulation and in-vivo training conditions.

  • Unfolding and learned ISTA: Each ISTA iteration becomes one learned-network layer, with model matrices replaced by trainable matrices P1 and P2 and a learned regularization parameter.Several such layers form the unfolded feedforward network.
  • Simulation results: CORONA recovers both UCA and tissue signals in simulations, while ResNet recovers the UCA signal but does not recover tissue.The CORONA recovery also has higher contrast than the ResNet recovery.
  • Training-data effects: Simulation-only training can overfit simulated patches, whereas additional in-vivo training improves performance on experimental data.The materials report that validation losses track training losses under simulation-only training, while combined training produces good in-vivo performance.
  • Training-data effects: Combined simulation and in-vivo training makes learned regularization parameters differ from those used by FISTA, often improving performance.Most regularization parameters change little after in-vivo training, but they do not converge to the iterative FISTA parameters.
  • In-vivo reconstruction: With sufficient simulation training, CORONA recovers experimental vascular structure, while combined training produces texture and visual quality more similar to non-learning methods.The materials describe 50 simulation epochs as sufficient for good experimental recovery and combined training as improving robustness to noise and modeling differences.

V. RUNTIME COMPARISON

The runtime comparison evaluates training and validation time for unfolded networks and ResNet, highlighting a depth-dependent trade-off between execution cost and performance.

  • Runtime comparison: The unfolded network trains and validates more slowly than ResNet; its 10-layer version is slower by an order of magnitude, while its 1-layer version is only slightly slower.The additional processing time is attributed to SVD operations required by the unfolded network.
  • Runtime comparison: The unfolded architecture allows a flexible trade-off between execution time and performance by varying its depth.The comparison also reports an order of magnitude fewer trainable parameters for the unfolded network.
  • Performance and training scope: The unfolded network achieves better CNR and CR values than ResNet in the reported comparison.ResNet was not fully trained; only its last fully connected layers were trained through transfer learning, reducing overall training time.
Loading 1811.08252v1…