字典学习。比如一个向量，是k维的，我现在有一个k*n的字典，其中n>>k，所谓的字典学习，就是在这包含n个向量的字典当中寻找一个线性表示可以表示出当前这个k维的向量。之所以称为“稀疏表示”，因为一般n大于k，比如n=512,k=64。这时候你的字典一定是一个Redundant（冗余的，过剩的）的。因此你的表示里面一定有很多系数为0，因而被称作稀疏表示。
信号稀疏表示的目的就是在给定的超完备字典中用尽可能少的原子来表示信号，可以获得信号更为简洁的表示方式，从而使我们更容易地获取信号中所蕴含的信息，更方便进一步对信号进行加工处理，如压缩、编码等。信号稀疏表示方向的研究热点主要集中在稀疏分解算法、超完备原子字典、和稀疏表示的应用等方面。(Dictionary study. For example, a vector is k dimension. I now have a dictionary of k*n, where n>>k, the so-called dictionary learning, is to find a linear expression in the dictionary containing N vectors, which can show the current vector of K dimension. It is called "sparse representation" because the general n is larger than k, such as n=512, k=64. At this time your dictionary must be a Redundant (redundant, excess). So there must be a lot of coefficients in your representation to be 0, so it's called a sparse representation.
Signal sparse representation is to overcomplete dictionary given in as little as possible to represent atomic signal, signal can be more succinct representation, which makes it easier for us to get there in the signal information, more convenient for further signal processing, such as compression, encoding etc.. The focus of r)