Multiscale higher-order TV operators for L1 regularization

Area of Science:

• Signal Processing
• Image Reconstruction
• Computational Imaging

Background:

• Traditional L1 regularization techniques are widely used for signal and image denoising and reconstruction.
• However, L1 formulations can introduce artifacts inconsistent with desired sparsity-promoting properties.
• Existing higher-order total variation (HOTV) methods aim to improve upon L1 but have limitations.

Purpose of the Study:

• To develop a novel multiscale higher-order total variation (MHOTV) approach for signal and image processing.
• To address the artifact generation issue observed in standard L1 regularization.
• To demonstrate the effectiveness of MHOTV in improving denoising and reconstruction quality, particularly for electron microscopy imaging.

Main Methods:

• Developed a multiscale higher-order total variation (MHOTV) method.
• Established a connection between MHOTV and multiscale Daubechies wavelets.
• Implemented efficient MHOTV computations using operator decomposition and Fourier space conversion.

Main Results:

• MHOTV demonstrates notable improvements over classical higher-order total variation (HOTV) and wavelet-based methods.
• The approach effectively reduces artifacts often seen with L1 regularization.
• Numerical results show the potential of MHOTV for enhancing 2D and 3D electron microscopy images.

Conclusions:

• MHOTV offers a superior alternative to existing regularization techniques for signal and image denoising and reconstruction.
• The established link between higher-order regularization and wavelets provides new insights into these methods.
• MHOTV shows significant promise for applications in advanced imaging, including electron microscopy.