There is provided a method of producing compressed data including the steps of receiving input data to be compressed (step 10), transforming said input data into a sum of basis functions multiplied by a corresponding set of coefficients, which may be a transformation to the frequency domain (step 12), forming a function or row of data from said set of coefficients (step 17), estimating the function using a learning process (step 21) and recording the resulting estimate (step 28) as the compressed data. Also provided is a method of estimating a function which may be used in the method of producing compressed data including inverting the function about a predetermined value (step 18) prior to using a learning process to estimate the function. Apparatus (1) for implementing the method and a software product to cause a processing means to implement the method are also claimed.