Very low bit rate image coding using redundant dictionaries

Abstract

Very low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in their multiscale nature and in their ability to sparsely represent functions that are piecewise smooth. Their main problem on the other hand, is that in 2-D wavelets are not able to deal with the natural geometry of images, i.e they cannot sparsely represent objects that are smooth away from regular submanifolds. In this paper we propose an approach based on building a sparse representation of images in a redundant geometrically inspired library of functions, followed by suitable coding techniques. Best N-term nonlinear approximations in general dictionaries is, in most cases, a NP-hard problem and sub-optimal approaches have to be followed. In this work we use a greedy strategy, also known as Matching Pursuit to compute the expansion. Finally the last step in our algorithm is an enhancement layer that encodes the residual image: in our simulation we have used a genuine embedded wavelet codec.

Image compression using an edge adapted redundant dictionary and wavelets

“…512×512 pixels). In [10] we obtained similar (but slightly worse in terms of PSNR) results with a less elaborated approach also based on Matching Pursuit. However, thanks to the use of the wavelets for coding the residual (see Sec.…”

“…The drawback of this method is that there is no more a guaranty that at each iteration the best atom will be selected as in the case of the full search MP. However the resulting loss in image quality is negligible [10].…”

“…In order to code the positions and projection coefficients, two different approaches can be taken into account. The first one consists of ordering the atoms in decreasing absolute projection values, then the projections can be quantized either in a differential way (DPCM) [10] or using an exponential quantizer [25]. The quantization is followed by arithmetic coding.…”

“…In this paper we use a technique based on the greedy Matching Pursuit algorithm that in general is not sparsenesspreserving [8]. However experimental results showed its ability to give highly sparse decompositions of 1-D signals [9], images [10,11] and videos [12,13]. Moreover very recent theoretical results prove that, under certain conditions, MP iteratively selects the atoms that give the sparsest representation.…”

Mixtures of boosted classifiers for frontal face detection

“…The filters are made of a combination of a Gaussian in one direction and its first derivative in the orthogonal direction and have been introduced by Peotta et al in [15] for image compression and signal approximation. The generating function φ : R 2 → R is given by:…”