We introduce a novel flexible approach to spatiotemporal exploration of rectilinear scalar volumes. Our out-of-core representation, based on per-frame levels of hierarchically tiled non-redundant 3D grids, efficiently supports spatiotemporal random access and streaming to the GPU in compressed formats. A novel low-bitrate codec able to store into fixed-size pages a variable-rate approximation based on sparse coding with learned dictionaries is exploited to meet stringent bandwidth constraint during time-critical operations, while a near-lossless representation is employed to support high-quality static frame rendering. A flexible high-speed GPU decoder and raycasting framework mixes and matches GPU kernels performing parallel object-space and image-space operations for seamless support, on fat and thin clients, of different exploration use cases, including animation and temporal browsing, dynamic exploration of single frames, and high-quality snapshots generated from near-lossless data. The quality and performance of our approach are demonstrated on large data sets with thousands of multi-billion-voxel frames.