Wavelet-based image compression

Many applications generate an exponentially increasing amount of information or data which needs to be stored, processed and transmitted in an efficient way. Typical information-intensive applications include spectral and high resolution image analysis. For example, a computerised axial tomography (CAT) image slice of size 512 x 512 and pixel depth (i.e. number of possible colours or grey-levels) of 8 bits occupies 0.25 MB of storage memory. For 60 such slices in a patient scan used in 3-D reconstruction, the total storage requirements is of the order of 15 MB. As a result of the possibly many stages involved in image analysis, each image in itself may generate other images, thereby further increasing the storage requirements for the image analysis procedure. For example, the raw CAT image slices can be processed to create a set of segmentated images used for interpretation such as volumetric analysis. Unfortunately, current storage hardware is inadequate for storing large amounts of such data as might be found in a patient database. Furthermore, if these data were to be transmitted over a network, the effective transmission times can be large. A solution is to employ compression techniques which may be capable of achieving a reduction in storage and transmission demands by a factor of more than 20 without significant loss in perceived image quality. Much of the information in a smooth image is highly correlated by virtue of the fact that, for example, pixel values are not spatially random and that the value of one pixel indicates the likelihood of its neighbours' values. Several types of correlation exist in an image: 1. Spatial correlation: Pixel values in a neighbourhood of a given pixel are generally similar. Exceptions include pixels in the neighbourhood of a pixel which forms the edge of an object in the image. 2. Sequential correlation: This occurs when two or more images are taken at different times (e.g. as a set of video frames) or different spatial positions (e.g. CAT image slices). The same pixel in adjacent image frames or slices is generally strongly correlated. 3. Spectral correlation: The spectral decomposition (Fourier transform) of an image is often smooth. Rapid fluctuations in the energy content of adjacent frequencies are uncommon. That is, spectral frequencies in a neighbourhood of frequencies are correlated. The presence of one or more of spatial, spectral and temporal correlations (and, therefore, the existence of an inherently high degree of redundancy) indicates that there exists a description of the image that has a significantly lower rank (for the definition of rank, see Chapter 4). That is, there exists in the image a set of features that captures most of the independent features. This suggests that an image is a good candidate for compression. Compression schemes can be broadly classified as loss-less or lossy compression. Loss-less compression schemes assume no loss of information during a compression-ciecompression cycle. This is most suited to data that need to be reconstructed exactly. Lossy compression schemes allow a certain error during a compression-ciecompression cycle, as long as the information loss is tolerable (i.e. the quality of the data is acceptable). The degree of tolerance to information loss is dictated by the particular application and some distortion metric appropriate to the application at hand is employed to measure the quality of the compression (see Section 2.1). For example, images which are used for simple visual display purposes can tolerate some loss as long as the images are psycho-visually acceptable. However, images that are used for segmentation or classification (e.g. medical or micro-fractographic industrial X-ray images) may not tolerate much information loss, particularly in the region of interest in the image. Lossy compression schemes have the advantage that a higher compression can be achieved compared with loss-less compression schemes. Most compression algorithms generally use a combination of both lossy and loss-less compression schemes with some facility made available to select the degree of loss of quality. In Section 2 we introduce the fundamentals of image compression and overview the various compression algorithms. We review the transformation techniques used in image compression in Section 3. Section 4 describes image compression using optimal task-based and best-basis image compression algorithms