Latent Variable Filtering for Unmixing Noisy and Undersampled Volumetric Images

Kernkonzepte

A method is proposed to map input volumetric measurements to a latent space where overlapping signal components are disentangled, enabling their isolation and quantification through the application of bandpass filters.

Zusammenfassung

The authors present a novel approach called "Latent Unmixing" for processing mixed images into their individual contributing components. The method uses a 3D U-Net convolutional neural network to combine the spatial and time/spectral dimensions of the input data, which is essential when each dimension alone does not contain enough information to allow correct separation of the components.

The key highlights and insights are:

1. The 3D U-Net is used to map the input volumetric data to a latent space where the different signal components are disentangled.
2. Predefined bandpass filters are then applied to the latent space to pool the disentangled components into separate output channels.
3. The method is demonstrated on three test cases: a variation of the MNIST dataset with simulated decay, fluorescence lifetime microscopy (FLIM), and mode decomposition in optical fibers.
4. For the MNIST dataset, the Latent Unmixing method outperforms the established Maximum Likelihood Estimation (MLE) approach, achieving high Pearson correlation between true and predicted pixel intensities.
5. In the FLIM experiments, Latent Unmixing shows better robustness to low photon counts and close lifetime values compared to the phasor analysis method.
6. For mode decomposition in multi-mode fibers, Latent Unmixing can retrieve the spatial distributions of the modes, even when the sampling frequency is below the Nyquist criterion.
7. The method is shown to generalize well to different types of input distributions, demonstrating its broad applicability.

Statistiken

The 3D-MNIST dataset was generated with the following parameters:

Signal-to-noise ratio (R) = 5
Decay constants: τ4 = 0.1, τ8 = 0.2, τ9 = 0.3, τb = 0.4
Time dimension histogram of L = 28 bins
The STED-FLIM dataset consists of 30 real microscopy images of four different proteins tagged with fluorescent markers in fixed cortical neurons. The images were split into 256 x 256 pixel crops, resulting in 1806 crops for training.
The S2-MMF dataset consists of simulated images of the intensity measured at the output of optical fibers for different input wavelengths. The dataset includes measurements with various combinations of up to 6 propagating modes, four different fiber geometries, and different mode-specific intensities. 1500 fiber measurements were used for training and 175 for testing.

Zitate

"Our method, called Latent Unmixing, transforms the overlapping input contributions to a latent space where they are untangled and can be separated by applying filters directly in the latent space."
"We chose to use a 3D U-Net for unmixing undersampled data so that the 3D kernels can combine essential information from neighboring pixels and neighboring time- or spectral-bins, since 3D convolution kernels allow the processing of all dimensions of a 3D input volume simultaneously."
"Our Latent Unmixing approach accurately predicts the pixel-wise contributions of 4 components on the test images in conditions where MLE and phasor approaches fail at correctly separating each channel."

Wichtige Erkenntnisse aus

Filtering Pixel Latent Variables for Unmixing Noisy and Undersampled Volumetric Images

by Cath... um arxiv.org 04-09-2024

https://arxiv.org/pdf/2312.05357.pdf

Tiefere Fragen

How could the Latent Unmixing method be extended to handle more complex input distributions, such as non-exponential decays or non-sinusoidal mode patterns

The Latent Unmixing method can be extended to handle more complex input distributions by adapting the network architecture and training process. For non-exponential decays, the network can be trained on datasets with different decay functions, allowing it to learn to map these varied distributions to the latent space. By incorporating a wider range of decay constants and shapes, the network can develop a more robust understanding of how to separate overlapping components with diverse decay profiles. Additionally, for non-sinusoidal mode patterns in multi-mode fibers, the network can be trained on simulated data with different spatial intensity distributions that reflect these patterns. By exposing the network to a variety of complex input distributions, it can learn to disentangle and separate the modes based on their unique spatial characteristics.

What other types of multi-dimensional data, beyond imaging, could benefit from the Latent Unmixing approach for signal separation and unmixing

Beyond imaging data, the Latent Unmixing approach can benefit a wide range of multi-dimensional datasets that require signal separation and unmixing. For example, in spectroscopy, where overlapping spectral signatures need to be resolved, the method can be applied to separate different chemical components in complex mixtures. In genomics, where gene expression data is measured across multiple dimensions, Latent Unmixing can help identify distinct gene expression patterns and separate overlapping signals from different genes. In financial data analysis, where multiple factors contribute to stock price movements, the method can be used to isolate and quantify the impact of each factor on the overall price fluctuations. Overall, any dataset with overlapping or complex signal components can benefit from the Latent Unmixing approach for effective separation and analysis.

Could the interpretability of the Latent Unmixing method, through the analysis of the pixel latent space distributions, be further leveraged to provide additional insights about the input data

The interpretability of the Latent Unmixing method, through the analysis of the pixel latent space distributions, can be further leveraged to provide additional insights about the input data. By examining the distribution of values in the latent space, researchers can gain insights into the network's confidence in its predictions. Regions of the latent space with well-separated distributions may indicate clear separation of components, while overlapping distributions may suggest uncertainty or ambiguity in the unmixing process. This analysis can help researchers identify challenging areas in the data where the network struggles to separate components accurately. Additionally, by analyzing the latent space distributions across different samples or datasets, researchers can identify patterns or trends in the unmixing process, leading to a deeper understanding of the data and the network's performance.