Latent fingerprint restoration is one of the most challenging problems for fingerprint identification. According to the current next-generation identification (NGI) system fact sheet, the number of unsolved latent fingerprint cases is more than a million and is increasing daily. The current state-of-the-art algorithms utilize various deep-learning networks to restore latent fingerprints in the spatial domain. Unfortunately, these algorithms faced difficulty recovering genuine friction ridges from low-quality latent fingerprints with complex backgrounds and noise. Instead of using deep-learning models to restore latent fingerprints directly in the spatial domain, we used the deep-learning model to predict a frequency-domain filter for restoring each latent input partitioning block. We integrated this new filter predictor model within a progressive feedback framework. As a result, the proposed method can reveal genuine friction ridges from complex backgrounds, especially around very low-quality areas and singular point areas, which is crucial to the success of latent fingerprint identification. We benchmarked our proposed method against state-of-theart methods with four public latent fingerprint datasets. In addition, we used one commercial-of-the-shelf (COTS) and another open-source fingerprint matchers in our benchmark. The experiments showed that the proposed method outperformed current state-of-the-art methods in identification accuracy. Compared to the state-of-the-art methods using deep learning in the spatial domain, the proposed method achieved an average rank-1 identification accuracy improvement of 3.75% and 3.19% of four public datasets with the COTS and open-source fingerprint matchers, respectively. Finally, the execution code was made publicly available for non-commercial purposes at https://github.com/skconan/SFP-Progressive-Feedback-Latent-Fingerprint-Restoration.