Image reconstruction by use of discrete cosine and related transforms

Abstract

A method for processing a field of image data samples to provide for one or more of the functions of decimation, interpolation, and sharpening is accomplished by use of an array transform processor such as that employed in a JPEG compression system. Blocks of data samples are transformed by the discrete even cosine transform (DECT) in both the decimation and interpolation processes, after which the number of frequency terms is altered. In the case of decimation, the number of frequency terms is reduced, this being followed by inverse transformation to produce a reduced-size matrix of sample points representing the original block of data. In the case of interpolation, additional frequency components of zero value are inserted into the array of frequency components after which inverse transformation produces an enlarged data sampling set without an increase in spectral bandwidth. In the case of sharpening, accomplished by a convolution or filtering operation involving multiplication of transforms of data and filter kernel in the frequency domain, there is provided an inverse transformation resulting in a set of blocks of processed data samples. The blocks are overlapped followed by a savings of designated samples, and a discarding of excess samples from regions of overlap. The spatial representation of the kernel is modified by reduction of the number of components, for a linear-phase filter, and zero-padded to equal the number of samples of a data block, this being followed by forming the discrete odd cosine transform (DOCT) of the padded kernel matrix.