Local cosine transform — a method for the reduction of the blocking effect in JPEG

Abstract

This paper presents the local cosine transform (LCT) as a new method for the reduction and smoothing of the blocking effect that appears at low bit rates in image coding algorithms based on the discrete cosine transform (DCT). In particular, the blocking effect appears in the JPEG baseline sequential algorithm.

Two types of LCT were developed: LCT-IV is based on the DCT type IV, and LCT-II is based on DCT type II, which is known as the standard DCT. At the encoder side the image is first divided into small blocks of pixels. Both types of LCT have basis functions that overlap adjacent blocks. Prior to the DCT coding algorithm a preprocessing phase in which the image is multiplied by smooth cutoff functions (or bells) that overlap adjacent blocks is applied. This is implemented by folding the overlap** parts of the bells back into the original blocks, and thus it permits the DCT algorithm to operate on the resulting blocks. At the decoder side the inverse LCT is performed by unfolding the samples back to produce the overlapped bells. The purpose of the multiplication by the bell is to reduce the gaps and inaccuracies that may be introduced by the encoder during the quantization step.

LCT-IV and LCT-II were applied on images as a preprocessing phase followed by the JPEG baseline sequential compression algorithm. For LCT-IV, the DCT type IV replaced the standard DCT as the kernel of the transform coding. In both cases, for the same low bit rates the blocking effect was smoothed and reduced while the image quality in terms of mean-square error became better. Subjective tests performed on a group of observers also confirm these results. Thus the LCT can be added as an optional step for improving the quality of existing DCT (JPEG) encoders. Advantages over other methods that attempt to reduce the blocking effect due to quantization are also described.