Set theoretic compression with an application to image coding

We show that the complete information that is available after an image has been encoded is not just an approximate quantized image version, but a whole set of consistent images that contains the original image by necessity. From this starting point, we develop a set of tools to design a new class of encoders for image compression, based on a set decomposition and recombination of image features. As an initial validation, we show the results of an experiment where these tools are used to modify the encoding process of block discrete cosine transform (DCT) coding in order to yield less blocking artifacts

Consistent Image Decoding from Multiple Lossy Versions

With the recent development of tools for data sharing in social networks and peer to peer networks, the same information is often stored in different nodes. Peer-to-peer protocols usually allow one user to collect portions of the same file from different nodes in the network, substantially improving the rate at which data are received by the end user. In some cases, however, the same multimedia document is available in different lossy versions on the network nodes. In such situations, one may be interested in collecting all available versions of the same document and jointly decoding them to obtain a better reconstruction of the original. In this paper we study some methods to jointly decode different versions of the same image. We compare different uses of the method of Projections Onto Convex Sets (POCS) with some Convex Optimization techniques in order to reconstruct an image for which JPEG and JPEG2000 lossy versions are available

Fractal compression and analysis on remotely sensed imagery

Remote sensing images contain huge amount of geographical information and reflect the complexity of geographical features and spatial structures. As the means of observing and describing geographical phenomena, the rapid development of remote sensing has provided an enormous amount of geographical information. The massive information is very useful in a variety of applications but the sheer bulk of this information has increased beyond what can be analyzed and used efficiently and effectively. This uneven increase in the technologies of gathering and analyzing information has created difficulties in its storage, transfer, and processing. Fractal geometry provides a means of describing and analyzing the complexity of different geographical features in remotely sensed images. It also provides a more powerful tool to compress the remote sensing data than traditional methods. This study suggests, for the first time, the implementation of this usage of fractals to remotely sensed images. In this study, based on fractal concepts, compression and decompression algorithms were developed and applied to Landsat TM images of eight study areas with different land cover types; the fidelity and efficiency of the algorithms and their relationship with the spatial complexity of the images were evaluated. Three research hypotheses were tested and the fractal compression was compared with two commonly used compression methods, JPEG and WinZip. The effects of spatial complexity and pixel resolution on the compression rate were also examined. The results from this study show that the fractal compression method has higher compression rate than JPEG and WinZip. As expected, higher compression rates were obtained from images of lower complexity and from images of lower spatial resolution (larger pixel size). This study shows that in addition to the fractal’s use in measuring, describing, and simulating the roughness of landscapes in geography, fractal techniques were useful in remotely sensed image compression. Moreover, the compression technique can be seen as a new method of measuring the diverse landscapes and geographical features. As such, this study has introduced a new and advantageous passageway for fractal applications and their important applications in remote sensing

Set theoretic compression with an application to image coding

We show that the complete information that is available after an image has been encoded is not just an approximate quantized image version, but a whole set of consistent images that contains the original image by necessity. From this starting point, we develop a set of tools to design a new class of encoders for image compression, based on a set decomposition and recombination of image features. As an initial validation, we show the results of an experiment where these tools are used to modify the encoding process of block discrete cosine transform (DCT) coding in order to yield less blocking artifacts. © 1998 IEEE