Recovering fine details from under-resolved electron tomography data using higher order total variation ℓ₁...

Area of Science:

• Electron microscopy and imaging science
• Computational imaging and image reconstruction
• Applied mathematics and signal processing

Background:

• Compressed sensing (CS) algorithms, particularly total variation (TV) regularization, have advanced electron tomography (ET) high-fidelity imaging.
• TV regularization effectively reduces noise and promotes piecewise constant solutions with sparse boundaries.
• Existing methods face limitations with complex image features and realistic tomographic sampling.

Purpose of the Study:

• To introduce and evaluate a novel ℓ1 regularization method, higher order total variation (HOTV), for electron tomography.
• To demonstrate HOTV's advantages over traditional TV regularization in image reconstruction.
• To assess HOTV's efficacy with pragmatic sampling patterns and fine image details.

Main Methods:

• Development of the higher order total variation (HOTV) regularization algorithm for electron tomography.
• Application of HOTV to both a real electron tomography dataset and a phantom dataset.
• Comparative analysis of HOTV against total variation (TV) and discrete tomography approaches.

Main Results:

• HOTV regularization enables more accurate reconstruction of a broader range of images compared to TV.
• HOTV effectively handles smooth regions without enforcing piecewise constant behavior, preserving finer image details.
• Demonstrated superior performance of HOTV with pragmatic tomographic sampling and complex image features.

Conclusions:

• Higher order total variation (HOTV) presents a significant advancement in electron tomography image reconstruction.
• HOTV overcomes limitations of TV regularization, particularly for images with intricate details and realistic data acquisition.
• The proposed HOTV method enhances the fidelity and accuracy of reconstructed electron tomography images.