Constructions Of Bidimensional Nonseparable Parseval Frames Associated With MRA

Let A be a 2×2 integer expand matrix (its eigenvalue's modulus is more than 1 and its entries are integers) and its determinant's absolute value is 2. Letψ(t)∈L2(R2),ψ(t) is called an A-dilation Parseval Frame wavelet if﹛A2/1(A1t-k):j∈Z,k∈Z2} is an A-dilation Parseval Frame for L2(R2). In this paper, we discuss construction methods of A-dilation nonseparable Parseval MRA Frame wavelets and character A-dilation Parseval Frame wavelets multipliers for L2(R2). There are six parts in the paper. The main results in the last two parts. We give a detail discussion on bidimensional nonseparable MRA Frame wavelets in the fifth part and give a numerical algorithm of bidimensional nonseparable MRA Frame wavelets with compact support in the last part. We also show the superiority of nonseparable Frame wavelets with compact support by contrasting them with separable frames in image processing.