Page 129 - Digital Analysis of Remotely Sensed Imagery

100 Cha pte r T h ree

During uncompression the decoder reconstructs an identical code
table directly from the compressed data as it decodes the encoded
data stream, without having to transmit the code table separately.
The original characters are restored from the compressed file by
taking a code at a time and by translating it to the character(s) it
represents in the code table.

3.4.4 Lossy Compression
Lossy compression is able to achieve a very high compression ratio at
the expense of losing a certain amount of information in the original
image. With some loss of information, the compression ratio can be
increased from lossless compression by tens of fold to 100:1 for single-
band imagery. Lossy compression technique is suitable for applications
that can tolerate some loss of information that is perceptually
insignificant. Occasionally the level of information loss may be able
to be specified prior to compression. Lossy compression differs from
error-free compression in that it involves a quantizer between the
symbol encoder and the stage when the prediction error is calculated.
The input to a quantizer can either be a scalar or vector. In the latter
case, it is called a vector quantizer.
Lossy compression may be implemented in one of three types:
lossy predictive coding, transform coding, and wavelet coding. In lossy
predictive coding the quantizer absorbs the nearest integer function of
the error-free encoder, between the symbol encoder and the point at
which the prediction error is formed. It establishes the relationship
between the degree of compression and distortion associated with
lossy predictive coding. In transform coding the input image is first
transformed linearly in a reversible fashion to decorrelate the pixel
values of each subimage or to pack as much information as possible
into the smallest set of transform coefficients. In a transform compression
the data resulting from a signal passing through the transform (e.g., the
discrete Fourier or cosine) will not have the same information-carrying
role. The transform coefficients are then quantized and coded. Those
coefficients that carry the least information are quantized at the coarsest
interval or truncated to zero. In this way a high compression ratio is
achieved without causing too much distortion to the image. The
encoding process consists of four steps of decomposition into
subimages, transformation, quantization, and coding. In the decoding
process these four steps are performed in the reversed order. Of the
various image transforms, discrete cosine transform is better at packing
information to the coefficients than others such as the discrete Fourier
transform. The most popular subimage sizes are 8 by 8 and 16 by 16. A
larger subimage size will cause both the level of compression and
computational complexity to increase.
In wavelet coding the pixel values of an input image are processed
via the wavelet transform function to remove any correlation among
them. Afterward the original image is decomposed into several