diff --git a/src/patch_denoise/bindings/cli.py b/src/patch_denoise/bindings/cli.py
index ea5890c..25bc64d 100644
--- a/src/patch_denoise/bindings/cli.py
+++ b/src/patch_denoise/bindings/cli.py
@@ -216,7 +216,17 @@ def _get_parser():
         type=IsFile,
         help=(
             "Phase of the input data. This MUST be in radians. "
-            "No conversion would be applied."
+            "No rescaling will be applied."
+        ),
+    )
+    data_group.add_argument(
+        "--noise-map-phase",
+        metavar="FILE",
+        default=None,
+        type=IsFile,
+        help=(
+            "Phase component of the noise map estimation file. "
+            "This MUST be in radians. No rescaling will be applied."
         ),
     )
 
@@ -283,17 +293,19 @@ def main():
 
     if args.input_phase is not None:
         input_data, affine = load_complex_nifti(args.input_file, args.input_phase)
-    input_data, affine = load_as_array(args.input_file)
+    else:
+        input_data, affine = load_as_array(args.input_file)
 
     kwargs = args.extra
 
     if args.nan_to_num is not None:
         input_data = np.nan_to_num(input_data, nan=args.nan_to_num)
+
     n_nans = np.isnan(input_data).sum()
     if n_nans > 0:
         logging.warning(
-            f"{n_nans}/{np.prod(input_data.shape)} voxels are NaN."
-            " You might want to use --nan-to-num=<value>",
+            f"{n_nans}/{input_data.size} voxels are NaN. "
+            "You might want to use --nan-to-num=<value>",
             stacklevel=0,
         )
 
@@ -302,14 +314,30 @@ def main():
         affine_mask = None
     else:
         mask, affine_mask = load_as_array(args.mask)
-    noise_map, affine_noise_map = load_as_array(args.noise_map)
+
+    if args.noise_map is not None and args.noise_map_phase is not None:
+        noise_map, affine_noise_map = load_complex_nifti(
+            args.noise_map,
+            args.noise_map_phase,
+        )
+    elif args.noise_map is not None:
+        noise_map, affine_noise_map = load_as_array(args.noise_map)
+    elif args.noise_map_phase is not None:
+        raise ValueError(
+            "The phase component of the noise map has been provided, "
+            "but not the magnitude."
+        )
+    else:
+        noise_map = None
+        affine_noise_map = None
 
     if affine is not None:
-        if affine_mask is not None and np.allclose(affine, affine_mask):
+        if (affine_mask is not None) and not np.allclose(affine, affine_mask):
             logging.warning(
                 "Affine matrix of input and mask does not match", stacklevel=2
             )
-        if affine_noise_map is not None and np.allclose(affine, affine_noise_map):
+
+        if (affine_noise_map is not None) and not np.allclose(affine, affine_noise_map):
             logging.warning(
                 "Affine matrix of input and noise map does not match", stacklevel=2
             )
@@ -344,7 +372,7 @@ def main():
         if noise_map is None:
             raise RuntimeError("A noise map must be specified for this method.")
 
-    denoised_data, patchs_weight, noise_std_map, rank_map = denoise_func(
+    denoised_data, _, noise_std_map, _ = denoise_func(
         input_data,
         patch_shape=args.patch_shape,
         patch_overlap=args.patch_overlap,
diff --git a/tests/test_spacetime_utils.py b/tests/test_spacetime_utils.py
index 4272fef..8131795 100644
--- a/tests/test_spacetime_utils.py
+++ b/tests/test_spacetime_utils.py
@@ -70,13 +70,30 @@ def f(x):
 
 
 @pytest.mark.parametrize("block_dim", range(5, 10))
-def test_noise_estimation(medium_random_matrix, block_dim):
-    """Test noise estimation."""
-    noise_map = estimate_noise(medium_random_matrix, block_dim)
-
-    real_std = np.nanstd(medium_random_matrix)
-    err = np.nanmean(noise_map - real_std)
-    assert err <= 0.1 * real_std
+def test_noise_estimation(block_dim):
+    """Test noise estimation.
+
+    The mean patch-wise standard deviation should be close to the overall
+    standard deviation.
+    """
+    for seed in range(15):
+        print(f"Seed: {seed}")
+        rng = np.random.RandomState(seed)
+        medium_random_matrix = rng.randn(200, 200, 100)
+        print(f"Mean of raw: {np.nanmean(medium_random_matrix)}")
+        print(f"Max of raw: {np.nanmax(medium_random_matrix)}")
+        print(f"Min of raw: {np.nanmin(medium_random_matrix)}")
+        real_std = np.nanstd(medium_random_matrix)
+        print(f"SD of raw: {real_std}")
+
+        noise_map = estimate_noise(medium_random_matrix, block_dim)
+        print(f"Mean of noise map: {np.nanmean(noise_map)}")
+        print(f"Max of noise map: {np.nanmax(noise_map)}")
+        print(f"Min of noise map: {np.nanmin(noise_map)}")
+        print(f"SD of noise map: {np.nanstd(noise_map)}")
+        err = np.nanmean(noise_map - real_std)
+        print(f"Err: {err}")
+        assert err <= 0.1 * real_std
 
 
 @parametrize_random_matrix