Adaptive regularized constrained least squares image restoration

In noisy environments, a constrained least-squares (CLS) approach is presen ted to restore images blurred by a Gaussian impulse response, where instead of choosing a global regularization parameter, each point in the signal ha s its own associated regularization parameter, These parameters are found b y constraining the weighted standard deviation of the wavelet transform coe fficients on the finest scale of the inverse signal by a function r which i s a local measure of the intensity variations around each point of the blur red and noisy observed signal. Border ringing in the inverse solution is pr oposed decreased by manipulating its wavelet transform coefficients on the finest scales close to the borders. If the noise in the inverse solution is significant, wavelet transform techniques are also applied to denoise the solution. Examples are given for images, and the results are shown to outpe rform the optimum constrained least-squares solution using a global regular ization parameter, both visually and in the mean squared error sense.