Laser driven inertial confinement fusion is a challenging research field in the current international frontier science, which uses high-energy laser as the driving source. A large amount of energy is injected into the target pellet to make the fusion material reach the state of high temperature and high density in a very short time, thus forming a hot spot in the center of the target pellet and igniting the whole fuel layer, and finally achieving controlled nuclear fusion. As the diameter of the implosion hot spot is about 50-100 μm, and its duration is 100-200 ps, the ion temperature reaches 5 keV, and the pressure can reach 4.0×10¹⁶ Pa. Therefore, it is of great significance to develop diagnostic techniques under extreme transient conditions. In this paper we introduce two kinds of diagnosis method based on compressed sensing. The first one combines the one-dimensional line Velocity interferometer system for any reflectors (VISAR) with the Compressed Ultrafast Photography (CPU) system, which is expected to achieve a new 2D-VISAR diagnostic technique with high time resolution. At the same time, it overcomes the shortcomings of the existing two-dimensional VISAR that can only capture single image and is expected to realize continuous diagnosis of the evolution of hydrodynamic instability. Because the existing CUP technology encoded by digital micromirror device can only be used in the visible light band, and cannot be used in the ultraviolet and X-ray band, a transmission compressed sensing technology is also developed. The transmission compressed sensing technology uses a novel transmission element to encode the measured signal, which can realize the two-dimensional ultrafast detection of ultraviolet and X-ray signals, and is expected to realize the precise diagnosis of the ultra-fast space-time evolution process of the hot spots in the explosion. In addition, in view of the advantages of single-channel CUP technology with high time resolution and the shortcomings of low spatial resolution, a new high spatial resolution diagnosis system with multi-channel coding, separate scanning, decoding and re-synthesis is proposed, which is expected to achieve high time resolution and high spatial resolution of the two-dimensional new diagnostic technology.