Building an X-ray Backscatter Imaging System with Compressed Sensing for Faster Image Reconstruction

Applied Science

Summary:

This video demonstrates an X-ray backscatter imaging system that uses a compressed sensing algorithm to reconstruct images from a small, randomly sampled subset of pixels, drastically reducing acquisition time. While traditional X-ray backscatter is slow, compressed sensing reduces acquisition time to 10-20 minutes by leveraging the property that natural images can be represented with a minimal number of unique frequencies, unlike random noise. The system features a custom gimbal mount with potentiometers and DC motors for precise control, and a sensitive detector system comprising a phosphor screen and a photomultiplier tube.

Introduction to Compressed Sensing and X-ray Backscatter [0:00:00]

• Compressed sensing is a technique that allows an image to be reconstructed from a small subset of its pixels [0:00:03].
  • It can reconstruct images with surprising fidelity even from only 10% of random samples [0:00:09].

    

  • This method can even reconstruct spatial frequencies higher than the Nyquist limit [0:00:18].
• The algorithm is applied to an X-ray backscatter imaging system [0:00:30].
  • This application is ideal because acquiring each pixel in X-ray backscatter is time-consuming, making it impractical to scan every pixel [0:00:38].

Understanding X-ray Backscatter Imaging [0:01:02]

• X-ray backscatter imaging is described as the closest thing to "true X-ray goggles" [0:01:05].
  • Unlike traditional X-ray shadowgrams, it does not require the detector to be behind the object [0:01:11].

    

• The imaging process involves shining a thin beam of X-rays into a scene and collecting the reflected (backscattered) X-rays [0:01:15].

  

  • Similar to how a laser pointer reflects differently off light vs. dark objects, X-rays scatter based on atomic number [0:01:25].
  • Lower atomic number elements (like hydrogen, carbon, oxygen) appear bright due to more backscatter [0:01:40].

    

  • Higher atomic number and dense elements appear dark because they absorb more X-rays [0:01:50].

    

• Challenges of X-ray Backscatter: [0:02:03]
  • The process is very lossy, requiring a tiny aperture (e.g., 400 microns) for high resolution [0:02:03].

    

  • Very few X-rays hit the object, and even fewer are reflected back to the detector, necessitating a super-sensitive, large-area detector [0:02:18].
  • Slow Acquisition Speed:
    • It takes about 8 milliseconds to collect enough photons for good dynamic range per pixel [0:02:58].
    • For an 800x800 pixel image with 1mm resolution and a 60-degree field of view, acquiring every pixel would take approximately 85 minutes [0:03:07].

      

    • Compressed sensing significantly reduces this time, potentially to 10-20 minutes for comparable quality by only acquiring a subset of pixels (e.g., one out of four) [0:04:12].
  • Motion Control Requirements:
    • Collecting every pixel requires incredibly precise pointing accuracy from the motion control system, which is difficult to control perfectly [0:03:30].
    • Randomness in sampling is beneficial for the compressed sensing algorithm [0:04:02].
  • Fundamental Resolution Limit:
    • Even with infinitesimally thin beams, X-rays penetrate materials, causing backscatter from various depths [0:04:58].
    • This penetration leads to a loss of resolution, as edges can appear blurred due to scattered X-rays from within the material [0:05:11].

      

    • There is a physical limit to how much resolution can be achieved, independent of hardware improvements [0:05:30].

Hardware and System Construction [0:05:49]

• Initial Concept (Handheld):
  • The idea was to handhold the X-ray tube and use an Inertial Measurement Unit (IMU) to measure angular rotation randomly [0:05:49].

    

  • This approach works because the compressed sensing algorithm benefits from random samples [0:06:02].
  • However, it's impractical for the 5-20 minutes of data collection required for a decent image, as it's hard to avoid missing areas manually [0:06:28].
• Gimbal Mount: [0:06:09]
  • The system uses a two-axis gimbal mount to control the X-ray tube's position [0:07:11].

    

  • Position Sensing: Analog potentiometers are used for absolute position sensing of both axes, offering stable readings even if power is cut [0:08:01].
  • Motion Control: DC gear motors control the position [0:08:27].
    • A small piece of latex helps ensure smooth gear meshing [0:08:30].
    • Originally, a 3D-printed TPU cog belt was considered but was too stretchy for the system's high inertia, leading to a direct gear connection [0:08:48].
    • Both axes use 3D-printed gears and sector gears [0:09:15].
• Detector System:
  • A 3D-printed black plastic structure houses a phosphor screen cut from an old X-ray intensifier cassette [0:09:32].

    

    • These screens convert X-rays into visible light, effectively exposing film or, in this case, a sensor [0:09:40].

      

  • A photomultiplier tube (PMT) detects the light from the phosphor screen [0:10:01].
  • A transimpedance amplifier converts the PMT's current pulses into voltage spikes [0:10:07].

    

• Control Electronics and Data Flow:
  • A Tinsy Arduino microcontroller coordinates the entire system [0:08:15].
  • The Tinsy 3.2's hardware analog comparator and counter efficiently count low-amplitude photon pulses (as small as 10-20 millivolts) without consuming CPU time [0:10:18].
  • The Tinsy controls the X-ray tube via an RS232 serial link, a task made easier by a programming manual found online [0:11:02].
    • X-ray supplies typically use analog control voltages for high voltage (e.g., 1V scales to 50kV) and current (e.g., 1V scales to 1mA) [0:11:31].
  • The Tinsy constantly reports potentiometer positions and photon counts (from the last 8ms) via USB serial to a computer [0:11:51].
  • A Processing.org script receives, plots, and saves this data to a CSV file [0:12:02].

    

  • The CSV file is then transferred to another computer for reconstruction using the compressed sensing algorithm [0:12:11].

    

    

• X-ray Safety:
  • The X-ray backscatter signal itself is very weak, requiring a photon counter to detect [0:12:21].
  • The primary concern is the strong primary X-ray beam, which is directed into the concrete floor [0:12:26].
  • Geiger counter measurements outside the shop confirmed no detectable radiation, treating the shop as the X-ray system's enclosure [0:12:33].

    

The "Magic" of Compressed Sensing Algorithm [0:12:41]

• The goal is to reconstruct an image from sparsely sampled points by finding the representation that uses the fewest number of unique frequencies [0:13:54, 0:14:01].
• One-Dimensional Analogy: [0:12:53]
  • Finding one frequency: If only one frequency created the points, one could brute-force search all possible frequencies to find the best fit [0:13:14].
  • Finding two frequencies: More complex, but still solvable by iterating through pairs of frequencies [0:13:30].
  • Finding the fewest frequencies: This becomes a challenging optimization problem with potentially infinite solutions, requiring a tuning parameter [0:13:54].

    

• Importance of Random Sampling:
  • Regular, equally spaced sampling (like traditional methods) can lead to "blind spots," making it impossible to distinguish between certain frequencies [0:14:46].
  • Completely random sampling is crucial because it eliminates these blind spots, allowing the algorithm to recover all frequency content [0:15:02].
• The "Natural Image" Property: [0:15:34]
  • A profound concept in information theory states that all "natural" images (photos, X-rays, microscope images, audio waveforms, etc.) share a fundamental property: they can be represented using a minimized number of unique frequencies [0:15:34, 0:15:52].
  • This contrasts sharply with "noise" images, which are random and require a vast number of frequencies to describe [0:16:07].

    

    

  • The sheer number of possible noise images is astronomically large, making it statistically impossible for a truly random image to look like a "real" image (e.g., a cat) [0:17:18, 0:18:04].

    

  • Therefore, the compressed sensing algorithm works by minimizing the likelihood of reconstructing a noise image (which represents the vast majority of possibilities) and maximizing the chance of reconstructing a real image (which is a tiny subset of possibilities) [0:18:20].
  • This is considered a universal law, not something human-made [0:18:50].

    

• Limitations and Edge Cases:
  • Images that are highly random, like a picture of sand where each grain is a pixel, can challenge the algorithm [0:19:14].
  • The algorithm operates on a "sliding scale"; it's not simply broken by edge cases but produces less ideal results [0:19:31].
  • The reconstructed images are not perfectly recreated because the algorithm doesn't know the exact missing data; it follows this universal law to infer the most probable real image [0:19:52].