Phase aberration is an inherent side effect of ultrasound imaging due to the speed of sound inhomogeneity nature of human tissues, resulting in focusing error and reduced image contrast. This work introduces a phase aberration correction technique by leveraging a point spread function (PSF) restoration filter. A convolutional neural network (CNN) is used to estimate phase-aberrated PSFs and design the restoration filter. In addition, we incorporate coherence index weighting, derived from the restoration filtering, to further suppress sidelobe energy. Evaluation using Field II-simulated phantoms showed clearer cyst borders and reduced sidelobe energy leakage after PSF restoration and filter-derived coherence weighting, leading to improvement in image contrast and quality.