Understanding CT Projection Data — Why .npy and What It Actually Means

CT projection data is just a NumPy array — but knowing exactly what that array means is the difference between debugging blind and understanding your pipeline.

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🗂️ Why .npy? — Storage Format Rationale

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.npy is the native binary serialization format for NumPy arrays. For numerical imaging data, it wins on almost every axis:

Key advantage: np.load() restores the exact array — shape, dtype, and memory layout — with zero parsing overhead and zero precision loss.

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Note: .npy is a raw binary dump. Loading it is essentially a memory-map read — the OS just points directly at the file bytes.

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When would you reach for something else?

• .h5 → bundle multiple arrays with metadata (e.g., projections + angles + geometry in one file)
• .tiff → interop with imaging tools like ImageJ or Fiji
• .mat → MATLAB compatibility

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🔢 The Shape of Projection Data

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Load your file and inspect it first:

import numpy as np
projections = np.load("projections.npy")
print(projections.shape, projections.dtype)
# e.g. (180, 512, 512)  float32

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The three axes map directly to CT geometry:

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Warning: For sparse-view CT, axis 0 is small by design — e.g., 60 angles instead of 720. The array is physically smaller, but the reconstruction problem becomes much harder.

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📐 What the Values Actually Represent

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Each value in the array is a line integral — the total X-ray attenuation accumulated along one ray path through the object.

$$p(\theta, t) = \int f(x, y) \, dl$$

Where:

• $f(x,y)$ — the object's attenuation map (what we want to reconstruct)
• $(\theta, t)$ — the projection angle and detector position
• The integral runs along the ray path

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In practice, raw detector readings $I$ are transformed via Beer-Lambert law:

$$p = -\log\left(\frac{I}{I_0}\right)$$

Where $I_0$ is the blank-scan (no object) intensity. This gives you the log-normalized sinogram — the standard input for reconstruction algorithms.

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Danger: Always check your data has been log-normalized before feeding it into FBP or your U-Net. Raw intensity values will produce garbage reconstructions.

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👁️ Visualising Your Data — Sanity Checks

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Two views every CT engineer should check:

import matplotlib.pyplot as plt

proj = np.load("projections.npy")

# 1. Single projection: one angle's detector image
plt.figure()
plt.imshow(proj[0], cmap='gray')
plt.title("Single Projection (angle 0)")
plt.colorbar()

# 2. Sinogram: all angles, one detector row slice
plt.figure()
plt.imshow(proj[:, proj.shape[1]//2, :], cmap='gray')
plt.xlabel("Detector column")
plt.ylabel("Projection angle")
plt.title("Sinogram (middle row)")
plt.colorbar()

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A healthy sinogram looks like smooth sinusoidal curves — hence the name. Each point in the object traces a sine wave across angles.

graph LR
    A["Object point\n(x, y)"] -->|"rotates through angles"| B["Traces a sinusoid\nin sinogram space"]
    B --> C["Radon Transform\np(θ, t)"]
    style A fill:#4A90D9,color:#fff
    style B fill:#E8A838,color:#fff
    style C fill:#5BA85A,color:#fff

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Tip: If your sinogram shows vertical stripes or gaps, that's your sparse-view problem — missing angles mean missing sinusoidal segments. Your reconstruction model needs to hallucinate those gaps intelligently.

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🧠 One-Sentence Intuition

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A .npy projection file is a 3D array of X-ray attenuation line integrals — indexed by angle, detector row, and detector column — and the sinogram is simply what one row of that array looks like when you stack all angles vertically.

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🔗 Where This Fits in the Sparse-View Pipeline

graph TD
    A["projections.npy\n(N_angles × H × W)"] --> B["FBP / FDK\nInitial Reconstruction"]
    B --> C["Sparse CT Volume\n(degraded, streaky)"]
    C --> D["3D U-Net\n+ Data Consistency Module"]
    D --> E["High-Quality\nReconstructed Volume"]
    style A fill:#4A90D9,color:#fff
    style B fill:#9B6EBD,color:#fff
    style C fill:#D9534F,color:#fff
    style D fill:#E8A838,color:#fff
    style E fill:#5BA85A,color:#fff

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Part of FYP notes series — Sparse-View CT Reconstruction. Next: FBP/FDK reconstruction and its limitations.