A recently developed method for the restoration of motion-blurred images is investigated and implemented for the special complicated case of image blur due to sinusoidal vibrations. Sinusoidal vibrations are analyzed in the context of blur identification and image restoration. The extent of the blur and the optical transfer function (OTF) are identified from the blurred image by a straightforward process without the use of iterative techniques. The blurred image is restored using a simple Wiener filter with the identified OTF. The main novel achievement is the use of only a single vibrated blurred image as input information, on which the restoration process, is based. The various cases of blur types that depend on the imaging conditions are considered. Examples of blur identification and image restoration are presented.