diff --git a/notebooks/example_ms.ipynb b/notebooks/example_ms.ipynb
new file mode 100644
index 0000000..28f008e
--- /dev/null
+++ b/notebooks/example_ms.ipynb
@@ -0,0 +1,60 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from bm3dornl.bm3d import bm3d_ring_artifact_removal_ms\n",
+    "from bm3dornl.denoiser_gpu import memory_cleanup\n",
+    "\n",
+    "with open(\"../../tests/bm3dornl-data/sino.npy\", \"rb\") as f:\n",
+    "    sino_noisy = np.load(f)\n",
+    "\n",
+    "memory_cleanup()\n",
+    "\n",
+    "block_matching_kwargs: dict = {\n",
+    "    \"patch_size\": (8, 8),\n",
+    "    \"stride\": 3,\n",
+    "    \"background_threshold\": 0.0,\n",
+    "    \"cut_off_distance\": (64, 64),\n",
+    "    \"num_patches_per_group\": 32,\n",
+    "    \"padding_mode\": \"circular\",\n",
+    "}\n",
+    "filter_kwargs: dict = {\n",
+    "    \"filter_function\": \"fft\",\n",
+    "    \"shrinkage_factor\": 3e-2,\n",
+    "}\n",
+    "kwargs = {\n",
+    "    \"mode\": \"simple\",\n",
+    "    \"k\": 4,\n",
+    "    \"block_matching_kwargs\": block_matching_kwargs,\n",
+    "    \"filter_kwargs\": filter_kwargs,\n",
+    "}\n",
+    "\n",
+    "sino_bm3dornl = bm3d_ring_artifact_removal_ms(\n",
+    "    sinogram=sino_noisy,\n",
+    "    **kwargs,\n",
+    ")\n",
+    "\n",
+    "\n",
+    "fig, axs = plt.subplots(1, 2, figsize=(12, 4))\n",
+    "axs[0].imshow(sino_noisy, cmap=\"gray\")\n",
+    "axs[0].set_title(\"Noisy sinogram\")\n",
+    "axs[1].imshow(sino_bm3dornl, cmap=\"gray\")\n",
+    "axs[1].set_title(\"BM3D denoised sinogram\")\n",
+    "plt.show()\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/src/bm3dornl/bm3d.py b/src/bm3dornl/bm3d.py
index 953bbd5..6b586e2 100644
--- a/src/bm3dornl/bm3d.py
+++ b/src/bm3dornl/bm3d.py
@@ -739,26 +739,46 @@ def bm3d_ring_artifact_removal_ms(
             filter_kwargs=filter_kwargs,
         )
 
-    # step 1: create a list of binned sinograms
-    binned_sinos = horizontal_binning(sinogram, k=k)
-    # reverse the list
-    binned_sinos = binned_sinos[::-1]
-
-    # step 2: estimate the noise level from the coarsest sinogram, then working back to the original sinogram
-    noise_estimate = None
-    for i in range(len(binned_sinos)):
-        logging.info(f"Processing binned sinogram {i+1} of {len(binned_sinos)}")
-        sino = binned_sinos[i]
-        sino_star = (
-            sino if i == 0 else sino - horizontal_debinning(noise_estimate, sino)
+    denoised_sino = None
+    # Make a copy of an original sinogram
+    sino_orig = horizontal_binning(sino_star, 1, dim=0)
+    binned_sinos_orig = [np.copy(sino_orig)]
+
+    # Contains upscaled denoised sinograms
+    binned_sinos = [np.zeros(0)]
+
+    # Bin horizontally
+    for i in range(0, k):
+        binned_sinos_orig.append(
+            horizontal_binning(binned_sinos_orig[-1], fac=2, dim=1)
         )
+        binned_sinos.append(np.zeros(0))
 
-        if i < len(binned_sinos) - 1:
-            noise_estimate = sino - bm3d_ring_artifact_removal(
-                sino_star,
-                mode=mode,
-                block_matching_kwargs=block_matching_kwargs,
-                filter_kwargs=filter_kwargs,
+    binned_sinos[-1] = binned_sinos_orig[-1]
+
+    for i in range(k, -1, -1):
+        logging.info(f"Processing binned sinogram {i + 1} of {k}")
+        # Denoise binned sinogram
+        denoised_sino = bm3d_ring_artifact_removal(
+            binned_sinos[i],
+            mode=mode,
+            block_matching_kwargs=block_matching_kwargs,
+            filter_kwargs=filter_kwargs,
+        )
+        # For iterations except the last, create the next noisy image with a finer scale residual
+        if i > 0:
+            debinned_sino = horizontal_debinning(
+                denoised_sino - binned_sinos_orig[i],
+                binned_sinos_orig[i - 1].shape[1],
+                2,
+                30,
+                dim=1,
             )
+            binned_sinos[i - 1] = binned_sinos_orig[i - 1] + debinned_sino
+
+    # residual
+    sino_star = sino_star + horizontal_debinning(
+        denoised_sino - sino_orig, sino_star.shape[0], fac=1, n_iter=30, dim=0
+    )
 
     return sino_star
diff --git a/src/bm3dornl/utils.py b/src/bm3dornl/utils.py
index 276a02e..4052cbf 100644
--- a/src/bm3dornl/utils.py
+++ b/src/bm3dornl/utils.py
@@ -2,8 +2,9 @@
 """Utility functions for BM3DORNL."""
 
 import numpy as np
-from scipy.interpolate import RectBivariateSpline
 from numba import njit
+from scipy.signal import convolve2d
+from scipy.interpolate import interp1d
 
 
 @njit
@@ -43,84 +44,130 @@ def is_within_threshold(
     return np.linalg.norm(ref_patch - cmp_patch) <= intensity_diff_threshold
 
 
-def horizontal_binning(Z: np.ndarray, k: int = 0) -> list[np.ndarray]:
+def create_array(base_arr: np.ndarray, h: int, dim: int):
     """
-    Horizontal binning of the image Z into a list of k images.
+    Create a padded and convolved array used in both binning and debinning.
+    Parameters
+    ----------
+    base_arr: Input array
+           h: bin count
+         dim: bin dimension (0 or 1)
+    Returns
+    -------
+    resulting array
+    """
+    mod_pad = h - ((base_arr.shape[dim] - 1) % h) - 1
+    if dim == 0:
+        pads = ((0, mod_pad), (0, 0))
+        kernel = np.ones((h, 1))
+    else:
+        pads = ((0, 0), (0, mod_pad))
+        kernel = np.ones((1, h))
+
+    return convolve2d(np.pad(base_arr, pads, "symmetric"), kernel, "same", "fill")
+
+
+def horizontal_binning(Z: np.ndarray, fac: int = 2, dim: int = 1) -> np.ndarray:
+    """
+    Horizontal binning of the image Z
 
     Parameters
     ----------
     Z : np.ndarray
         The image to be binned.
-    k : int
-        Number of iterations to bin the image by half.
-
+    fac : int
+        binning factor
+    dim : direction X=0, Y=1
     Returns
     -------
-    list[np.ndarray]
-        List of k images.
+    np.ndarray
+        binned image
 
-    Example
-    -------
-    >>> Z = np.random.rand(64, 64)
-    >>> binned_zs = horizontal_binning(Z, 3)
-    >>> len(binned_zs)
-    4
     """
-    binned_zs = [Z]
-    for _ in range(k):
-        sub_z0 = Z[:, ::2]
-        sub_z1 = Z[:, 1::2]
-        # make sure z0 and z1 have the same shape
-        if sub_z0.shape[1] > sub_z1.shape[1]:
-            sub_z0 = sub_z0[:, :-1]
-        elif sub_z0.shape[1] < sub_z1.shape[1]:
-            sub_z1 = sub_z1[:, :-1]
-        # average z0 and z1
-        Z = (sub_z0 + sub_z1) * 0.5
-        binned_zs.append(Z)
-    return binned_zs
-
-
-def horizontal_debinning(original_image: np.ndarray, target: np.ndarray) -> np.ndarray:
+
+    if fac > 1:
+        fac_half = fac // 2
+        binned_zs = create_array(Z, fac, dim)
+
+        # get coordinates of bin centres
+        if dim == 0:
+            binned_zs = binned_zs[
+                fac_half + ((fac % 2) == 1) : binned_zs.shape[dim] - fac_half + 1 : fac,
+                :,
+            ]
+        else:
+            binned_zs = binned_zs[
+                :,
+                fac_half + ((fac % 2) == 1) : binned_zs.shape[dim] - fac_half + 1 : fac,
+            ]
+
+        return binned_zs
+
+    return Z
+
+
+def horizontal_debinning(
+    Z: np.ndarray, size: int, fac: int, n_iter: int, dim: int = 1
+) -> np.ndarray:
     """
     Horizontal debinning of the image Z into the same shape as Z_target.
 
     Parameters
     ----------
-    original_image : np.ndarray
+    Z : np.ndarray
         The image to be debinned.
-    target : np.ndarray
-        The target image to match the shape.
+    size: target size (original size before binning) for the second dimension
+    fac: binning factor (original divisor)
+    n_iter: number of iterations
+    dim: dimension for binning (Y = 0 or X = 1)
 
     Returns
     -------
     np.ndarray
         The debinned image.
-
-    Example
-    -------
-    >>> Z = np.random.rand(64, 64)
-    >>> target = np.random.rand(64, 128)
-    >>> debinned_z = horizontal_debinning(Z, target)
-    >>> debinned_z.shape
-    (64, 128)
     """
-    # Original dimensions
-    original_height, original_width = original_image.shape
-    # Target dimensions
-    new_height, new_width = target.shape
-
-    # Original grid
-    original_x = np.arange(original_width)
-    original_y = np.arange(original_height)
-
-    # Target grid
-    new_x = np.linspace(0, original_width - 1, new_width)
-    new_y = np.linspace(0, original_height - 1, new_height)
-
-    # Spline interpolation
-    spline = RectBivariateSpline(original_y, original_x, original_image)
-    interpolated_image = spline(new_y, new_x)
+    if fac <= 1:
+        return np.copy(Z)
+
+    fac_half = fac // 2
+
+    if dim == 0:
+        base_array = np.ones((size, 1))
+    else:
+        base_array = np.ones((1, size))
+
+    n_counter = create_array(base_array, fac, dim)
+
+    # coordinates of bin counts
+    x1c = np.arange(fac_half + ((fac % 2) == 1), (Z.shape[dim]) * fac, fac)
+    x1 = np.arange(fac_half + 1 - ((fac % 2) == 0) / 2, (Z.shape[dim]) * fac, fac)
+
+    # coordinates of image pixels
+    ix1 = np.arange(1, size + 1)
+
+    interpolated_image = 0
+
+    for j in range(max(1, n_iter)):
+        # residual
+        if j > 0:
+            residual = Z - horizontal_binning(interpolated_image, fac, dim)
+        else:
+            residual = Z
+
+        # interpolation
+        if dim == 0:
+            interp = interp1d(
+                x1,
+                residual / n_counter[x1c, :],
+                kind="cubic",
+                fill_value="extrapolate",
+                axis=0,
+            )
+        else:
+            interp = interp1d(
+                x1, residual / n_counter[:, x1c], kind="cubic", fill_value="extrapolate"
+            )
+        interpolated_image = interpolated_image + interp(ix1)
 
     return interpolated_image
 
diff --git a/tests/unit/bm3dornl/test_bm3d_ring_artifact_removal_ms.py b/tests/unit/bm3dornl/test_bm3d_ring_artifact_removal_ms.py
index bcf9e92..895f5d6 100644
--- a/tests/unit/bm3dornl/test_bm3d_ring_artifact_removal_ms.py
+++ b/tests/unit/bm3dornl/test_bm3d_ring_artifact_removal_ms.py
@@ -1,53 +1,36 @@
 import pytest
-from unittest.mock import patch
 import numpy as np
 from bm3dornl.bm3d import bm3d_ring_artifact_removal_ms
 
 
+size_x = 256
+size_y = 256
+
+
 @pytest.fixture
 def setup_sinogram():
-    return np.random.rand(256, 256)
+    return np.random.rand(size_x, size_y)
 
 
-@patch("bm3dornl.bm3d.horizontal_binning")
-@patch("bm3dornl.bm3d.horizontal_debinning")
-@patch("bm3dornl.bm3d.bm3d_ring_artifact_removal")
+@pytest.mark.cuda_required
 def test_bm3d_ring_artifact_removal_ms(
-    mock_bm3d_ring_artifact_removal,
-    mock_horizontal_debinning,
-    mock_horizontal_binning,
     setup_sinogram,
 ):
     sinogram = setup_sinogram
-    binned_sinos = [np.random.rand(64, 64) for _ in range(4)]
-    mock_horizontal_binning.return_value = binned_sinos
-    binned_sinos = [np.random.rand(64, 64) for _ in range(4)]
-    mock_bm3d_ring_artifact_removal.return_value = binned_sinos
-    binned_sinos = [np.random.rand(64, 64) for _ in range(4)]
-    mock_horizontal_debinning.return_value = binned_sinos
 
     result = bm3d_ring_artifact_removal_ms(sinogram, k=4)
 
     assert result is not None
-    mock_horizontal_binning.assert_called_once_with(sinogram, k=4)
-    assert mock_bm3d_ring_artifact_removal.call_count == 3
-    assert mock_horizontal_debinning.call_count == 3
+
+    r, c = result.shape
+
+    assert c == size_x
+    assert r == size_y
 
     result_single_pass = bm3d_ring_artifact_removal_ms(sinogram, k=0)
     assert result_single_pass is not None
-    mock_bm3d_ring_artifact_removal.assert_called_with(
-        sinogram,
-        mode="simple",
-        block_matching_kwargs={
-            "patch_size": (8, 8),
-            "stride": 3,
-            "background_threshold": 0.0,
-            "cut_off_distance": (64, 64),
-            "num_patches_per_group": 32,
-            "padding_mode": "circular",
-        },
-        filter_kwargs={
-            "filter_function": "fft",
-            "shrinkage_factor": 3e-2,
-        },
-    )
+
+    r, c = result_single_pass.shape
+
+    assert c == size_x
+    assert r == size_y
diff --git a/tests/unit/bm3dornl/test_utils.py b/tests/unit/bm3dornl/test_utils.py
index 49000a5..2df4783 100644
--- a/tests/unit/bm3dornl/test_utils.py
+++ b/tests/unit/bm3dornl/test_utils.py
@@ -46,39 +46,22 @@ def test_is_within_threshold():
 
 
 def test_horizontal_binning():
+    size_x, size_y = 64, 64
+    k = 6
     # Initial setup: Create a test image
-    Z = np.random.rand(64, 64)
-
-    # Number of binning iterations
-    k = 3
-
-    # Perform the binning
-    binned_images = horizontal_binning(Z, k)
-
-    # Assert we have the correct number of images
-    assert len(binned_images) == k + 1, "Incorrect number of binned images returned"
+    Z = np.random.rand(size_y, size_y)
 
     # Assert that each image has the correct dimensions
-    expected_width = 64
-    for i, img in enumerate(binned_images):
-        assert img.shape[0] == 64, f"Height of image {i} is incorrect"
-        assert img.shape[1] == expected_width, f"Width of image {i} is incorrect"
+    expected_width = size_x
+    for i in range(k):
+        # Perform the binning
         expected_width = (expected_width + 1) // 2  # Calculate the next expected width
-
-
-def test_horizontal_binning_k_zero():
-    Z = np.random.rand(64, 64)
-    binned_images = horizontal_binning(Z, 0)
-    assert len(binned_images) == 1 and np.array_equal(
-        binned_images[0], Z
-    ), "Binning with k=0 should return only the original image"
-
-
-def test_horizontal_binning_large_k():
-    Z = np.random.rand(64, 64)
-    binned_images = horizontal_binning(Z, 6)
-    assert len(binned_images) == 7, "Incorrect number of images for large k"
-    assert binned_images[-1].shape[1] == 1, "Final image width should be 1 for large k"
+        binned_image = horizontal_binning(Z, fac=2)
+        assert binned_image.shape[0] == 64, f"Height of image {i} is incorrect"
+        assert (
+            binned_image.shape[1] == expected_width
+        ), f"Width of image {i} is incorrect"
+        Z = binned_image
 
 
 @pytest.mark.parametrize(
@@ -87,7 +70,9 @@ def test_horizontal_binning_large_k():
 def test_horizontal_debinning_scaling(original_width, target_width):
     original_image = np.random.rand(64, original_width)
     target_shape = (64, target_width)
-    debinned_image = horizontal_debinning(original_image, np.empty(target_shape))
+    debinned_image = horizontal_debinning(
+        original_image, target_width, fac=2, dim=1, n_iter=1
+    )
     assert (
         debinned_image.shape == target_shape
     ), f"Failed to scale from {original_width} to {target_width}"