Image restorations for single degradations have been widely studied, demonstrating excellent performance for each degradation, but can not reflect unpredictable realistic environments with unknown multiple degradations, which may change over time. To mitigate this issue, image restorations for known and unknown multiple degradations have recently been investigated, showing promising results, but require large networks or have sub-optimal architectures for potential interference among different degradations. Here, inspired by the filter attribution integrated gradients (FAIG), we propose an adaptive discriminative filter-based model for specific degradations (ADMS) to restore images with unknown degradations. Our method allows the network to contain degradation-dedicated filters only for about 3% of all network parameters per each degradation and to apply them adaptively via degradation classification (DC) to explicitly disentangle the network for multiple degradations. Our proposed method has demonstrated its effectiveness in comparison studies and achieved state-of-the-art performance in all-in-one image restoration benchmark datasets of both Rain-Noise-Blur and Rain-Snow-Haze.