Image Compression in Noise

Abstract

Use of the CSF in Image Compression The visual system’s variations in sensitivity to spatial frequencies are critical to any imaging system where the image is to be displayed and viewed by a human observer. These variations are described by the contrast sensitivity function (CSF) which has found wide application in image compression schemes using the discrete cosine transform (DCT) [1-3], vector quantization [4], and spatial filter hierarchies [5]. All of these approaches provide access to the frequency domain, and the use of the CSF becomes straightforward in controlling the quantization process of the algorithm. Quantization is used to code the algorithm coefficients or vectors; an increase in the size of the quantization interval reduces the entropy, and thus the bit rate. However, larger quantization intervals increase the quantization error of the algorithm, which can be regarded as noise that will degrade the image if it is visible. This quantization noise must be detected in the presence of the effective internal noise of the visual system, which is proportional to the inverse of the CSF. Therefore, the inverse CSF can be used to scale the quantization intervals, allowing larger intervals for frequencies where the visual system is less sensitive and smaller intervals where it is more sensitive. If, for all frequencies, the maximum error of the frequency specific quantization noise is kept less than the effective internal noise of the frequency, the compressed image will be visually indistinguishable from the uncompressed image. We refer to this condition as perceptually lossless, as opposed to mathematically lossless, in which the digital code values are exactly preserved. Since the bit rates for perceptually lossless compression are less than a quarter of those for mathematically lossless compression, perceptually lossless compression is a useful criterion when the image is to be viewed by human observers.