Analysis and comparison of various image downsampling and upsampling methods

Summary form only given. The goal is to gain a better understanding of the behavior of the image down/upsampling combinations, and find better down/upsampling methods. We examined existing down/upsampling methods and proposed new ones. We formulated a frequency response approach for understanding and evaluating down/upsampling combinations. The approach was validated experimentally by running the methods on various images and computing the signal to noise ratio (SNR) between the original and the down-then-upsampled images. The frequency response based evaluation correlates well with the experimental evaluation. Down/upsampling combinations were studied in a unified framework. Signals are pre-filtered then decimated by two, resulting in downsampling by two. Afterwards, signals are zero-upsampled by 2, i.e., inserting 0s between successive samples, and then post-filtering. Our analysis showed that for optimal performance, the pre-filter and the post-filter should both be low-pass filters with cutoff at π/2. We considered five classes of filters. The first corresponds to the simplest down/upsampling combination, decimation/duplication, where decimation is simply the skipping of every other row and every other column, and duplication (for upsampling) involves duplicating every row and every column. The second class corresponds to bilinear interpolation, for both upsampling and downsampling. The third class comprises the biorthogonal and orthogonal wavelets. The fourth class we termed binomial filters. The fifth class consists of least-square FIR filters