Final answer:
The question relates to using Matlab's iradon function for image reconstruction with various filters and angle stepping. Different filters affect the frequency responses and hence the quality of the reconstructed image. Angle stepping affects data sampling density which influences the resolution and speed of reconstruction.
Step-by-step explanation:
The subject of the student's question concerns the use of Matlab's iradon function for backprojection in image reconstruction, typically used within the field of computed tomography (CT). The various filters mentioned such as 'Ram-Lak', 'Shepp-Logan', 'Cosine', 'Hamming', and 'Hann' are applied during the reconstruction process to refine the image quality. Angle stepping refers to the incremental rotation of the imaging apparatus around the subject or the incremental sampling of projection angles in synthetic data.
When using the Matlab function iradon, various filters can be applied to the reconstructed image to improve resolution and noise. The filters modify the frequency components of the Radon transform, each having unique characteristics that affect the reconstructed image differently. For example, the Ram-Lak filter, also known as the Ramp filter, is a high-pass filter that accentuates the high-frequency components enhancing edges, but may also amplify noise. The Shepp-Logan filter is similar but includes a window that reduces the high-frequency boost, aiming to provide a smoother image. The Cosine filter multiplies the Fourier transform of the projection data by a cosine function, emphasizing certain frequencies. The Hamming and Hann filters are types of frequency windows that suppress higher frequencies to reduce noise at the cost of some resolution.
Different angle steps affect the sampling density of the projection data. Smaller steps such as 1° provide denser data, potentially leading to higher-quality reconstructions, but require more computational resources and time. In contrast, larger steps such as 10° may result in faster reconstruction but with the possibility of lower resolution and artifact presence.