Recent developments in frame theory

Frames are the generalizations of orthonormal basis in Hilbert spaces. As for an or-thonormal basis, a frame allows each element x ∈ L²(ℝ) to be written as x = ∑c_nx_n, for suitable coefficients {c_n}; however, in contrast to the situation for a basis, the coefficients might not be unique. We present the basic facts from the frame theory and the corresponding results for Gabor frames, wavelet frames and wave packet systems are discussed. Most of the paper is a survey of literature, notably the work given in [7, 8, 19, 23]. As an application of tight wavelet frames, known as framelets, we have used it for deblurring of images.