The Compton effect describes the interaction of x-ray photons with electrons, in Compton's experiment in 1922/23 the electrons of graphite atoms. The x-ray photons scatter (Compton scattering) off the electrons in different directions. The remaining energy (lower frequency) of the scattered x-ray photons depends on the scattering angle. From an energy based point of view, these 'new or old' photons are a part of the original energy, represented by the incident x-ray photon before the interaction. The photons loss of energy (reduced frequency) is gained by an electron. Depending on this energy the electron could leave the atom. Depending on the remaining energy of the photon the interaction can repeat with a more to more decreasing energy level in the form of further Compton Scattering or by photo-electric absorption. Usually the Compton effect involves atom-bound electrons.
The Compton effect is responsible for most scattering effects in radiography.

Imaging refers to the visual representation of an object. Today, diagnostic imaging uses radiology and other techniques, mostly noninvasive, to create pictures of the human body. Diagnostic radiography studies the anatomy and physiology to diagnose an array of medical conditions. The history of medical diagnostic imaging is in many ways the history of radiology. Many imaging techniques also have scientific and industrial applications. Diagnostic imaging in its widest sense is part of biological science and may include medical photography, microscopy and techniques which are not primarily designed to produce images (e.g., electroencephalography and magnetoencephalography).
Brief overview about important developments:
Imaging used for medical purposes, began after the discovery of x-rays by Konrad Roentgen 1896. The first fifty years of radiological imaging, pictures have been created by focusing x-rays on the examined body part and direct depiction onto a single piece of film inside a special cassette.
In the 1950s, first nuclear medicine studies showed the up-take of very low-level radioactive chemicals in organs, using special gamma cameras. This diagnostic imaging technology allows information of biologic processes in vivo. Today, single photon emission computed tomography (SPECT) and positron emission tomography (PET) play an important role in both clinical research and diagnosis of biochemical and physiologic processes.
In the 1960s, the principals of sonar were applied to diagnostic imaging. Ultrasound has been imported into practically every area of medicine as an important diagnostic tool, and there are great opportunities for its further development. Looking into the future, the grand challenges include targeted contrast imaging, real-time 3D or 4D ultrasound, and molecular imaging. The earliest use of ultrasound contrast agents (USCA) was in 1968.
The introduction of computed tomography (CT/CAT) in the 1970s revolutionized medical imaging with cross sectional images of the human body and high contrast between different types of soft tissues. These developments were made possible by analog to digital converters and computers. First, spiral CT (also called helical), then multislice CT (or multi-detector row CT) technology expanded the clinical applications dramatically.
The first magnetic resonance imaging (MRI) devices were tested on clinical patients in 1980. With technological improvements including higher field strength, more open MRI magnets, faster gradient systems, and novel data-acquisition techniques, MRI is a real-time interactive imaging modality that provides both detailed structural and functional information of the body.

Today, imaging in medicine has been developed to a stage that was inconceivable a century ago, with growing modalities:
x-ray projection imaging, including conventional radiography and digital radiography;
All these types of scans are an integral part of modern healthcare. Usually, a radiologist interprets the images. Most clinical studies are acquired by a radiographer or radiologic technologist. In filmless, digital radiology departments all images are acquired and stored on computers. Because of the rapid development of digital imaging modalities, the increasing need for an efficient management leads to the widening of radiology information systems (RIS) and archival of images in digital form in a picture archiving and communication system (PACS). In telemedicine, medical images of MRI scans, x-ray examinations, CT scans and ultrasound pictures are transmitted in real time.

See also Interventional Radiology, Image Quality and CT Scanner.

(DR) Digital radiography uses a special electronic x-ray detector, which converts the radiographic image into a digital picture for review on a computer monitor. The digital image is then stored and can be post processed by changing the magnification, orientation, brightness, and contrast. Digital radiography (also called direct radiography) is a progressive development of computed radiography (CR).
These advantages can lead to fewer 'recalls' (repeated x-ray images) including a lower radiation dose than analog or conventional radiography. DR and CR systems use no chemicals to process the x-ray images and the hazardous materials and waste associated with film development are eliminated.

Advantages of digital radiography compared with conventional radiography:

The half value layer (also half value thickness) is the amount of absorbing material, which is needed to reduce the x-ray intensity by one half.
The half value layer provides important information about the energy characteristics of the radiation. A low (or thin) half value layer for a given x-ray beam indicates that the x-ray beam contains more low energy and less penetrating radiation. An x-ray beam containing high energy or highly penetrating radiation has a high (or thick) half value thickness.

An imaging plate is used in computed radiography (CR) instead of a conventional film cassette.
The imaging plate is coated with photostimulable phosphors. The phosphor layer is doped with special substances to alter the crystalline structure and physical properties. After radiation, the enhanced phosphor material absorbs and stores x-ray energy in gaps of the crystal structure, building a latent image.
Usually, the storage phosphors are stimulated with a low-energy laser to release visible light at each point of x-ray absorption. To read-out the image, the plate is inserted into a computed radiography scanner. The scanning laser beam causes the electrons to relax to lower energy levels, emitting light that is captured by a photo-multiplier tube and converted into an electrical signal. The electronic signal is then converted to digital data and can be displayed on laser-printed films, workstations, transmitted to remote systems, and stored digitally.
The CR units automatically erase the image plate after the complete scan. Phosphor imaging plates, like film, are stored in cassette format and can be re-used very often if they are handled carefully. Existing conventional x-ray equipment, from generators to x-ray tubes and examination systems, can be used with imaging plates.