Multi-resolution imaging

ROTIR supports a coarse-to-fine reconstruction strategy using the hierarchical structure of HEALPix. Starting at a low resolution, the reconstruction is progressively refined by upsampling and re-optimizing at each level.

Why multi-resolution?

At high HEALPix resolution (n=4 or 5), the optimizer faces a high-dimensional problem with many local minima. Starting from a coarse solution and refining helps:

• Faster convergence: fewer pixels at low resolution means fewer iterations
• Better global minimum: coarse features are established first
• Robust regularization: the effective regularization adapts to each scale

Using multires_reconstruct_oi

using ROTIR

# Load data
oifitsfiles = ["epoch1.oifits", "epoch2.oifits"]
data_all = readoifits_multiepochs(oifitsfiles)
data = data_all[1, :]
tepochs = [d.mean_mjd for d in data] .- data[1].mean_mjd

star_params = (
    surface_type=2, rpole=1.37, tpole=4800.0, ldtype=3, ld1=0.23, ld2=0.0,
    inclination=78.0, position_angle=24.0, rotation_period=54.8,
    beta=0.08, frac_escapevel=0.9, B_rot=0.0,
)

tmap, stars = multires_reconstruct_oi(data, star_params, tepochs;
                                       n_start=2, n_end=4,
                                       maxiter=500, reg_weight=1e-5,
                                       reg_type="tv2", verbose=true)

This runs reconstruction at HEALPix levels n=2, 3, 4:

At each level, the map from the previous level is upsampled (each HEALPix pixel splits into 4 children) and used as the starting point.

Keywords

Additional keywords are passed through to image_reconstruct_oi (e.g., lower, upper).

Manual multi-resolution

For more control, you can manually upsample and reconstruct at each level:

# Level n=2
n = 2
tessels = tessellation_healpix(n)
stars = create_star_multiepochs(tessels, star_params, tepochs)
tmap = parametric_temperature_map(star_params, stars[1])
setup_oi!(data, stars)
regularizers = [["tv2", 1e-5, tv_neighbors_healpix(n), 1:length(tmap)]]
tmap = image_reconstruct_oi(tmap, data, stars; maxiter=500, regularizers=regularizers)

# Upsample to level n=3
tmap, stars = upsample_map_stars(tmap, stars, star_params, tepochs)
setup_oi!(data, stars)
n = 3
regularizers = [["tv2", 1e-5, tv_neighbors_healpix(n), 1:length(tmap)]]
tmap = image_reconstruct_oi(tmap, data, stars; maxiter=500, regularizers=regularizers)

# Upsample to level n=4
tmap, stars = upsample_map_stars(tmap, stars, star_params, tepochs)
setup_oi!(data, stars)
n = 4
regularizers = [["tv2", 1e-5, tv_neighbors_healpix(n), 1:length(tmap)]]
tmap = image_reconstruct_oi(tmap, data, stars; maxiter=500, regularizers=regularizers)

Downsampling

To reduce resolution (e.g., for quick visualization or comparison):

tmap_coarse, stars_coarse = downsample_map_stars(tmap, stars, star_params, tepochs)

Each group of 4 child pixels is averaged into one parent pixel.