Automatic music transcription (AMT) is the process of converting an acoustic musical signal into a symbolic musical representation, such as a MIDI file, which contains the pitches, the onsets and offsets of the notes and, possibly, their dynamics and sources (i.e., instruments). Most existing algorithms for AMT operate in the frequency domain, which introduces the well known time/frequency resolution trade-off of the Short Time Fourier Transform and its variants. In this paper, we propose a time-domain transcription algorithm based on an efficient convolutional sparse coding algorithm in an instrumentspecific scenario, i.e., the dictionary is trained and tested on the same piano. The proposed method outperforms a current state-of-the-art AMT method by over 26% in F-measure, achieving a median Fmeasure of 93.6%, and drastically increases both time and frequency resolutions, especially for the lowest octaves of the piano keyboard.