An array of data values, such as an image of pixel values, is stored in a main memory (12). A processing operation is performed using the pixel values. The processing operation defines time points of movement of a multidimensional region (20, 22) of locations in the image. Pixel values from inside and around the region are cached for processing. At least when a cache miss occurs for a pixel value from outside the region, cache replacement of data in cache locations (142) is performed. Locations that store pixel data for locations in the image outside the region (20, 22) are selected for replacement, selectively exempting from replacement cache locations (142) that store pixel data locations in the image inside the region. In embodiments, different types of cache structure are used for caching data values inside and outside the region. In an embodiment the cache locations for pixel data inside the regions support a higher level of output parallelism than the cache locations for pixel data around the region. In a further embodiment the cache for locations inside the region contains sets of banks, each set for a respective line from the image, data from the lines being distributed in a cyclically repeating fashion over the banks.