New One-Dimensional Transforms

Encoding data includes: determining multiple patterns for computing one-dimensional transforms over a first array of data elements. Each pattern includes multiple subsets of data elements of the first array. Each subset included in a first pattern has substantially the same number of data elements as each of the other subsets included in the first pattern. Each data element of the first array is included in a single one of the subsets included in the first pattern. At least one subset included in the first pattern consists of data elements that are not in a contiguous sequence along a single dimension. Encoding the data includes: computing, for each pattern, multiple one-dimensional transforms over data elements of respective subsets included in the pattern; selecting a set of transform coefficients from a group of multiple sets of transform coefficients; and encoding the selected set of transform coefficients to represent the first array.