Medical Images

Aim

After completing the course:

• The student should be able to explain the basic theory for 1D and 2D continuous Fourier transform with associated theorems, sampling, reconstruction, and DFT. The student should be able to explain the basic theory of digital images (two-dimensional signals), for example, 2D discrete convolution, resampling, interpolation, and some classic image analysis. The student should be able to explain simple convolution kernels and filters for derivation, low-pass, and high-pass filtering. The student should be able to perform related calculations.
• The student should be able to explain the most common types of medical images, what they show, and their underlying physics and technology: CT, X-ray, MRI, ultrasound, gamma camera, SPECT, and PET. The student should have a deeper understanding of the above-mentioned techniques by performing related calculations with a focus on signal and image processing.
• The student should be able to analyze and perform calculations on images, using a high-level language such as Python and/or Matlab. This includes interpreting the results of 1D and 2D Fourier transforms, as well as simulating how a medical image (CT, MRI, ultrasound) is created.

Content

The course consists of 2 parts. The first part intends to provide basic knowledge of signal processing on images. In the second part, this knowledge is used to understand how images are created with CT, MRI, ultrasound, SPECT, and PET.

1) Basic signal processing on images:

• The digital image. Histograms and grayscale transformations. Color tables.
• Repetition of the 1D Fourier transform. From 1D to 2D Fourier transform. Theorems for 1D and 2D Fourier transform, such as scaling, translation, derivative, convolution, and multiplication. Theorems for 2D Fourier transform such as the rotation and projection theorem. Look at images and their Fourier transforms and relate these to the theorem.
• The Dirac pulse. Sampling and reconstruction. Effects on the image in the case of aliasing in the spatial or Fourier domain.
• 1D and 2D DFT. Discrete 1D and 2D convolution. Convolution kernels in spatial and Fourier domain: low pass (Gaussian), high pass (Laplace), derivative (Sobel).
• 2D geometric operations. Resampling and interpolation. Projection and back-projection.
• Some basic image analysis methods such as thresholding, erosion, and labeling.
• Measurements and noise on images, such as contrast, resolution, MTF, and SNR.

2) Some common medical imaging techniques with a focus on signal and image processing:

• CT and X-ray. Basic physics about the X-ray spectrum, physical interaction such as the photoelectric effect, coherent and incoherent scattered radiation, etc. This physics is addressed to show its impact on the images. 2D reconstruction with the direct Fourier method and filtered back-projection. Fanbeam and rebinning. Briefly about 3D reconstruction and iterative reconstruction.
• MRI. Basic physics about e.g. spin, precession, RF pulse, and gradients to understand how an image is created through measurements in the k-space (2D Fourier domain). Orientation on different variants of MRI such as fMRI, EPI, and diffusion.
• Ultrasound. How is a B-mode ultrasound image created? RF data, envelope detection with quadrature filter, grayscale transformation, downsampling, scan conversion (resampling), etc.
• SPECT, PET, and the gamma camera: Basic physics of the interaction of gamma photons in the patient and the collimator, the principle of PET, i.e. positron+electron= 2 opposing gamma photons, etc. The gamma camera. Iterative reconstruction with the ML-EM algorithm. Image examples of SPECT-CT and PET-CT.

The computer exercises:

• 1) The digital image: pixels/size/zoom, quantization, and storage, grayscale/color, real/complex. Histogram and grayscale transformations. Color tables: grayscale, RGB true, pseudo. 2-D Fourier transform of the images: appearance, properties. Simple convolution kernels in the spatial domain. Linear filters in the Fourier domain.
• 2) Resampling and interpolation. Effects of sampling in the spatial and Fourier domain.
• 3) CT reconstruction: How do you do a CT image?
• 4) Basic MRI. Design of pulse sequences.
• 5) How do you do an ultrasound image? Rf-signal => envelope detection => downsampling => histogram transformation => scan conversion (resampling) => ultrasound image
• 6) Measurement of noise. Some simple image analysis methods. Preparation for computer exercise 7.
• 7) Measurements on SPECT/CT volumes. Example volumes from healthy and COPD patients.

Study visit: The course includes a study visit to CMIV, where we will look at a CT scanner and an MRI camera. We will also listen to a lecture about how medical images are used today at the University Hospital in Linköping. If necessary, the study visit can be virtual and/or via Zoom.