Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.Introduction. -In various fields of science and technology, such as earth observation, astronomy, medicine, civil engineering, materials science, and in compiling image databases [1], it has a major relevance to recover original signals from deficient signals obtained by limited number of measurements. The Nyquist-Shannon sampling theorem [2] provides the necessary and sufficient number of measurements for recovering arbitrary band-limited signals. However, techniques based on this theorem sometimes do not match restrictions and/or demands of today's front-line applications [3,4], and much effort is still being made to find more efficient methodologies.