COMPRESSED SENSING AND SOME IMAGE PROCESSING APPLICATIONS

Abstract: We live in a digital media-overloaded world. An enormous number of images, sound and video files are continuously being created and either transmitted over the internet or stored on hard drives or portable storage devices. During their transmission or storage, however, such digital files are almost without an exception subjected to a process of discarding most of their original information, since e.g. fast opening of a web site image or a small audio file size are today of utmost importance. Loss in redundant or imperceptible information is therefore inevitable and incorporated in lossy compression algorithms such as JPEG, MPEG or MP3, but to record raw video or audio data only to be, in large part, soon discarded during the process of sending it to a receiver is obviously not an optimum approach. Compressed sensing is a signal processing technique that provides one solution to the above problem. Rather than performing acquisition followed by compression of a signal, it combines both steps in a single sensing – or sampling – operation. In other words, compressed sensing allows acquiring signals while taking only a few samples. One of the underlying assumptions of the signal is that it is sparse, i.e. it should be possible to represent it with a matrix, consisting of a large number of zero – or close to zero – coefficients. Images, when represented in a non-spatial domain, such as discrete cosineor wavelet-domain, often comply with such a requirement. Theory behind the compressed sensing will be presented briefly together with several examples of successful implementation of this method in the field of signal – mainly image – processing.