3/1/2023 0 Comments Unshaky software![]() Convolution is thus a very specific and relatively simple mathematical process and, as such, it is quite remarkable that so many natural degradations can be described by this same process. However, convolution is commutative - this means that f can just as correctly be described as the PSF w.r.t. Given this description, h is conventionally called the point spread function (or PSF) because it determines how each and every point in f is 'spread out' into a copy of the PSF. This is why convolution is sometimes also known as the superposition integral and deconvolution is sometimes also called signal separation. The process of convolution is often represented by an asterisk (*). All these copies are then superimposed onto each other to create the resulting convolved signal ( g - see the figure below). Each such copy has overall integrated intensity equal to the intensity of the single point in f from which it was made. In essence, every point in signal 1 (call this f) is converted into a copy of signal 2 (call this h). Convolution is a process that 'mixes-up' two signals is a specific way. ![]() Now for some information about convolution.Ĭonvolution and the Point Spread Function (PSF) Given that deconvolution 'undoes' convolution, we need to understand what convolution is if we are to fully understand deconvolution. ![]() Further examples will also be given as you explore the results shown in this website. For more details on this example visit the 'Results' page of where you can see an animation of the deconvolution process and learn more about deconvolution artefacts and how to minimise them. This is an example of deconvolution artefacts that are an unwanted 'side-effect' of deconvolution. Note also that there are some speckles in the restored image not seen in the original test card. Now, if you refer back to the top of this page, the image on the right is the result of applying a deconvolution algorithm to the blurred image and shows that much of the fine detail of the test card has been restored. ![]() This original testcard is shown here on the right. On the left is a blurred version of a 'test card' image made by embellishing a stylised letter 'A' with some dots, lines and highlights and with a variable grey background. As deconvolution is a process that tries to find the state of a signal before some degradation occurred, starting from the degraded signal, deconvolution can be categorised as a solution to an inverse problem and the mathematics of inverse problems are relevant to understanding and devising deconvolution algorithms.Īn example of image deconvolution is seen in the figure at the top of this page. When dealing with digital images we speak of image restoration or, the more specific, image deconvolution. Deconvolution is thus a specific example of a restoration process. Processes designed to remove degradations from signals in general (not just convolutional degradations) are called 'restoration' processes. camera shake), diffraction blur and many others. However, convolutional degradations describe many of the degradations we meet in practice such as out-of-focus blurring, motion blur (e.g. There are other types of degradations but deconvolution cannot help with those. The types of degradations that deconvolution aims to reverse are specifically those which may be described by a mathematical process called convolution. a series of 3D volumes taken at sequential time points). microscope through-focus volumes or 'Z-stacks'), or higher dimensional signals (e.g. infrared spectra or sound waveforms), 2-dimensional (e.g. The following paragraphs give a brief overview of the subject with some key words linked to Wikipedia articles for forensic analysis of CCTV footage or in other situations where you cannot easily go back and take the picture again. The ability to re-focus a blurred image after it has been taken (using computational means) can be extremely useful e.g. to remove blurring from a photograph that was originally taken with the wrong focus (or with camera shake). What is Deconvolution? Deconvolution is a process designed to remove certain degradations from signals e.g.
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