Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform.

Area of Science:

• X-ray imaging
• Phase contrast imaging
• Interferometry

Background:

• X-ray Talbot moiré interferometers generate differential phase images.
• Conventional phase integration methods are unstable and cause detail loss.
• High-resolution imaging requires stable phase reconstruction.

Purpose of the Study:

• To develop a stable reconstruction method for X-ray differential phase imaging.
• To overcome limitations of conventional phase integration techniques.
• To preserve high-resolution details and avoid directional bias in images.

Main Methods:

• Utilizing the inverse Riesz transform for phase reconstruction.
• Developing Riesz transform theory for differential phase data.
• Comparing inverse Riesz results with integrated phase and phase gradient modulus.

Main Results:

• The inverse Riesz transform provides a stable reconstruction.
• The method retains high-resolution details without directional bias.
• Experimental X-ray differential phase data validated the approach.

Conclusions:

• The inverse Riesz transform offers a stable and effective method for X-ray differential phase imaging.
• This approach enhances image quality by preserving fine details.
• The method is computationally efficient, implemented via Fourier domain complex multiplication.