Sparse Recovery Using Sparse Random Matrices

Over the recent years, a new *linear* method for compressing high-dimensional data (e.g., images) has been discovered. For any high-dimensional vector x, its *sketch* is equal to Ax, where A is an m x n matrix (possibly chosen at random). Although typically the sketch length m is much smaller than the number of dimensions n, the sketch contains enough information to recover an *approximation* to x. At the same time, the linearity of the sketching method is very convenient for many applications, such as data stream computing and compressed sensing.