Declipping of Audio Signals Using Perceptual Compressed Sensing

The restoration of clipped audio signals, commonly known as declipping, is important to achieve an improved level of audio quality in many audio applications. In this paper, a novel declipping algorithm is presented, jointly based on the theory of compressed sensing (CS) and on well-established properties of human auditory perception. Declipping is formulated as a sparse signal recovery problem using the CS framework. By additionally exploiting knowledge of human auditory perception, a novel perceptual compressed sensing (PCS) framework is devised. A PCS-based declipping algorithm is proposed which uses ℓ₁-norm type reconstruction. Comparative objective and subjective evaluation experiments reveal a significant audio quality increase for the proposed PCS-based declipping algorithm compared to CS-based declipping algorithms.

I. Introduction

Clipping introduces undesired signal distortion in many audio applications. Clipping can occur both in the analog domain and in the digital domain, and is generally caused by the inability of an audio playback, recording or processing device to deliver the dynamic range required by the audio signal. When a digital audio signal is clipped¹

In the context of this research, digital hard clipping is considered, and it will be simply termed “clipping” throughout this paper. Note that in analogue systems, soft clipping is very common.

, all its sample values lying beyond a maximum amplitude level (referred to as the clipping level ) are mapped onto , as shown in Fig. 1.