Constrained least-squares image restoration: an improved computational scheme

In this short paper we present an improved computational technique to solve the Fredholm integral equation of the first kind which arises in image restoration and other inverse filtering applications. The technique is based on the works of Phillips, Twomey, and Hunt. We show that when the integral represents a convolution, the integral equation can be solved iteratively with each iteration requiring O(n) operations, where n is the number of sample points or observations. When there are p iterations to find the final solution to the integral equation, the present technique is approximately (1 + p/4) times faster than the implementation suggested by Hunt. In image processing application areas where p has been observed to be between 3 and 12, the technique can reduce computation by a factor of 2 to 4.