This paper presents a method for the recognition of Glagolitic characters in degraded historical documents. The Glagolitic character recognition is based on Dense SIFT for which image restoration is proposed as a pre-processing step in order to suppress background noise in degraded documents. Two different methods for image restoration are used which are Total Variation regularization and a new restoration method. Each method performs robustly against background noise while preserving character edges and strokes in the documents defected by stain, bleed through, and faded out ink. The experimental results achieved on three datasets show that by using image restoration as a pre-processing step to Dense SIFT generates better recognition rates for Glagolitic characters in degraded documents.