ℓ1 Trend Filter for Image Denoising

Abstract

The major problem in digital image processing is the presence of unwanted frequencies(noise). In this paper ℓ1 trend filter is proposed as an image denoising technique. ℓ1-trend filter estimates the hidden trend in the data by formulating a convex optimization problem based on ℓ1 norm. The proposed method extends the application of ℓ1 trend filter from one dimensional signals to three dimensional color images. Here the filter is applied over the image in a cascade, initially filtering along the rows followed by filtering along the columns. This identifies the hidden image information from the noisy image resulting in a smooth or denoised image. The proposed method is compared with the wavelet denoising technique using the quality metrics Peak-Signal-to-Noise-Ratio(PSNR) and Structural Similarity Index(SSIM).