Projected Barzilai-Borwein method for large-scale nonnegative image restoration

Image restoration refers to minimizing the degradation caused by the sensor environment, such as misfocused CCD cameras, nonuniform motions, atmospheric aerosols, and atmospheric turbulences. In image restoration problems, it is reasonable to add nonnegative constraints because of the physical meaning of the image. Then, the problem can be expressed as a quadratic programming problem with nonnegative constraints. However, in previous research, a parameterization technique is needed to reduce the problem into an unconstrained optimization problem. To avoid parameterization techniques, we apply the recently developed projected Barzilai-Borwein (PBB) method to solve this quadratic programming problem. Also, a novel approach for reducing the cost of matrix-vector multiplication is proposed when applying BB and PBB methods for atmospheric image restoration. The numerical experiments show that this method is promising for large-scale image restoration problems.