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Image restoration is the operation of taking a corrupt/noisy image and estimating the clean, original image. Corruption may come in many forms such as motion blur, noise and camera mis-focus. [1] Image restoration is performed by reversing the process that blurred the image and such is performed by imaging a point source and use the point source image, which is called the Point Spread Function (PSF) to restore the image information lost to the blurring process.
Image restoration is different from image enhancement in that the latter is designed to emphasize features of the image that make the image more pleasing to the observer, but not necessarily to produce realistic data from a scientific point of view. Image enhancement techniques (like contrast stretching or de-blurring by a nearest neighbor procedure) provided by imaging packages use no a priori model of the process that created the image.
With image enhancement noise can effectively be removed by sacrificing some resolution, but this is not acceptable in many applications. In a fluorescence microscope, resolution in the z-direction is bad as it is. More advanced image processing techniques must be applied to recover the object.
The objective of image restoration techniques is to reduce noise and recover resolution loss. Image processing techniques are performed either in the image domain or the frequency domain. The most straightforward and a conventional technique for image restoration is deconvolution, which is performed in the frequency domain and after computing the Fourier transform of both the image and the PSF and undo the resolution loss caused by the blurring factors. Nowadays, photo restoration is done using digital tools and software to fix any type of damage images may have and improve the general quality and definition of the details.
1. Geometric correction
2. Radiometric correction
3. Denoising
Image restoration techniques aim to reverse the effects of degradation and restore the image as closely as possible to its original or desired state. The process involves analysing the image and applying algorithms and filters to remove or reduce the degradations. The ultimate goal is to enhance the visual quality, improve the interpretability, and extract relevant information from the image.
Image restoration can be broadly categorized into two main types: spatial domain and frequency domain methods. Spatial domain techniques operate directly on the image pixels, while frequency domain methods transform the image into the frequency domain using techniques such as the Fourier transform, where restoration operations are performed. Both approaches have their advantages and are suitable for different types of image degradation.
Spatial domain techniques primarily operate on the pixel values of an image. Some common methods in this domain include:
This technique replaces each pixel value with the median value in its local neighborhood, effectively reducing impulse noise.
Based on statistical models, the Wiener filter minimizes the mean square error between the original image and the filtered image. It is particularly useful for reducing noise and enhancing blurred images.
This technique minimizes the total variation of an image while preserving important image details. It is effective in removing noise while maintaining image edges.
Frequency domain techniques involve transforming the image from the spatial domain to the frequency domain, typically using the Fourier transform. Some common methods in this domain include:
This technique aims to recover the original image by estimating the inverse of the degradation function. However, it is highly sensitive to noise and can amplify noise in the restoration process.
By incorporating constraints on the solution, this method reduces noise and restores the image while preserving important image details.
It is used for enhancing images that suffer from both additive and multiplicative noise. This technique separately processes the low-frequency and high-frequency components of the image to improve visibility.
Image restoration has a wide range of applications in various fields, including:
In criminal investigations, image restoration techniques can help enhance surveillance footage, recover details from low-quality images, and improve the identification of objects or individuals.
Image restoration is crucial in medical imaging to improve the accuracy of diagnosis. It helps in reducing noise, enhancing contrast, and improving image resolution for techniques such as X-ray, MRI, CT scans, and ultrasound.
Image restoration techniques are commonly used in digital photography to correct imperfections caused by factors like motion blur, lens aberrations, and sensor noise. They can also be used to restore old and damaged photographs.
Image restoration plays a significant role in preserving historical documents, artworks, and photographs. By reducing noise, enhancing faded details, and removing artifacts, valuable visual content can be preserved for future generations. [2]
Despite significant advancements in image restoration, several challenges remain. Some of the key challenges include handling complex degradations, dealing with limited information, and addressing the trade-off between restoration quality and computation time.
The future of image restoration is likely to be driven by developments in deep learning and artificial intelligence. Convolutional neural networks (CNNs) have shown promising results in various image restoration tasks, including denoising, super-resolution, and inpainting. The use of generative adversarial networks (GANs) has also gained attention for realistic image restoration.
Additionally, emerging technologies such as computational photography and multi-sensor imaging are expected to provide new avenues for image restoration research and applications.
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.
Halftone is the reprographic technique that simulates continuous-tone imagery through the use of dots, varying either in size or in spacing, thus generating a gradient-like effect. "Halftone" can also be used to refer specifically to the image that is produced by this process.
Digital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing. Since images are defined over two dimensions digital image processing may be modeled in the form of multidimensional systems. The generation and development of digital image processing are mainly affected by three factors: first, the development of computers; second, the development of mathematics ; third, the demand for a wide range of applications in environment, agriculture, military, industry and medical science has increased.
In digital signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts (aliasing) when representing a high-resolution image at a lower resolution. Anti-aliasing is used in digital photography, computer graphics, digital audio, and many other applications.
Microscope image processing is a broad term that covers the use of digital image processing techniques to process, analyze and present images obtained from a microscope. Such processing is now commonplace in a number of diverse fields such as medicine, biological research, cancer research, drug testing, metallurgy, etc. A number of manufacturers of microscopes now specifically design in features that allow the microscopes to interface to an image processing system.
In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the signal-to-noise ratio (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem.
Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio.
Homomorphic filtering is a generalized technique for signal and image processing, involving a nonlinear mapping to a different domain in which linear filter techniques are applied, followed by mapping back to the original domain. This concept was developed in the 1960s by Thomas Stockham, Alan V. Oppenheim, and Ronald W. Schafer at MIT and independently by Bogert, Healy, and Tukey in their study of time series.
The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system. The PSF in many contexts can be thought of as the extended blob in an image that represents a single point object, that is considered as a spatial impulse. In functional terms, it is the spatial domain version of the optical transfer function (OTF) of an imaging system. It is a useful concept in Fourier optics, astronomical imaging, medical imaging, electron microscopy and other imaging techniques such as 3D microscopy and fluorescence microscopy.
Super-resolution imaging (SR) is a class of techniques that enhance (increase) the resolution of an imaging system. In optical SR the diffraction limit of systems is transcended, while in geometrical SR the resolution of digital imaging sensors is enhanced.
In image processing, a Gaussian blur is the result of blurring an image by a Gaussian function.
Optical resolution describes the ability of an imaging system to resolve detail, in the object that is being imaged. An imaging system may have many individual components, including one or more lenses, and/or recording and display components. Each of these contributes to the optical resolution of the system; the environment in which the imaging is done often is a further important factor.
The stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation-invariance of the discrete wavelet transform (DWT). Translation-invariance is achieved by removing the downsamplers and upsamplers in the DWT and upsampling the filter coefficients by a factor of in the th level of the algorithm. The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input – so for a decomposition of N levels there is a redundancy of N in the wavelet coefficients. This algorithm is more famously known as "algorithme à trous" in French which refers to inserting zeros in the filters. It was introduced by Holschneider et al.
In computer graphics and digital imaging, imagescaling refers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement.
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are captured or transmitted. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain. A variant, the modulation transfer function (MTF), neglects phase effects, but is equivalent to the OTF in many situations.
The image fusion process is defined as gathering all the important information from multiple images, and their inclusion into fewer images, usually a single one. This single image is more informative and accurate than any single source image, and it consists of all the necessary information. The purpose of image fusion is not only to reduce the amount of data but also to construct images that are more appropriate and understandable for the human and machine perception. In computer vision, multisensor image fusion is the process of combining relevant information from two or more images into a single image. The resulting image will be more informative than any of the input images.
Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The contourlet transform has a fast implementation based on a Laplacian pyramid decomposition followed by directional filterbanks applied on each bandpass subband.
In signal processing it is useful to simultaneously analyze the space and frequency characteristics of a signal. While the Fourier transform gives the frequency information of the signal, it is not localized. This means that we cannot determine which part of a signal produced a particular frequency. It is possible to use a short time Fourier transform for this purpose, however the short time Fourier transform limits the basis functions to be sinusoidal. To provide a more flexible space-frequency signal decomposition several filters have been proposed. The Log-Gabor filter is one such filter that is an improvement upon the original Gabor filter. The advantage of this filter over the many alternatives is that it better fits the statistics of natural images compared with Gabor filters and other wavelet filters.
In multidimensional signal processing, Multidimensional signal restoration refers to the problem of estimating the original input signal from observations of the distorted or noise contaminated version of the original signal using some prior information about the input signal and /or the distortion process. Multidimensional signal processing systems such as audio, image and video processing systems often receive as input, signals that undergo distortions like blurring, band-limiting etc. during signal acquisition or transmission and it may be vital to recover the original signal for further filtering. Multidimensional signal restoration is an inverse problem, where only the distorted signal is observed and some information about the distortion process and/or input signal properties is known. A general class of iterative methods have been developed for the multidimensional restoration problem with successful applications to multidimensional deconvolution, signal extrapolation and denoising.
Video super-resolution (VSR) is the process of generating high-resolution video frames from the given low-resolution video frames. Unlike single-image super-resolution (SISR), the main goal is not only to restore more fine details while saving coarse ones, but also to preserve motion consistency.