High Quality Content by WIKIPEDIA articles! The flexibility of the overcomplete frame is one of its key advantages when used in expressing a signal or approximating a function. However, because of this redundancy, a function can have multiple expressions under an overcomplete frame [6]. When the frame is finite, the decomposition can be expressed as f=Ax , where f is the function we want to approximate, A is the matrix containing all the elements in the frame, and x is the coefficients of f under the representation of A. Without any other constraint, the frame will choose to give x with minimal norm in L2(R). Based on this, some other properties may also be considered when solving the equation, such as sparsity. So different researchers have been working on solving this equation by adding other constraints in the objective function. For example, a constraint minimizing x's norm in L1(R) may be used in solving this equation.

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