Multi-Scale Dictionary Learning Using Wavelets

Ophir, Boaz; Lustig, Michael; Elad, Michael

doi:10.1109/jstsp.2011.2155032

Cited by 148 publications

(85 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As suggested in Ophir et al work [1].The wavelet based dictionary learning can further utilize the sparsity between the wavelet coefficients: …”

Section: Methodology 21 Nonlocal Hierarchical Dictionarymentioning

confidence: 99%

“…There are three orientations: LH, HL, and HH. In each orientation, patches with the size m × m are extracted from all the sub bands in all different scales with maximum overlapping (similar to the grouping that has been suggested in [1]). One benefit of this variation is that the number of the training samples in a single orientation is larger than that in a decomposition level, mainly for lower sub bands.…”

Section: Methodology 21 Nonlocal Hierarchical Dictionarymentioning

confidence: 99%

See 1 more Smart Citation

Nonlocal Hierarchical Dictionary Learning using Wavelets and Gradient Histogram Preservation for Image Denoising: A Review

Prajapati¹,

Gyanchandani²

2015

IJCA

View full text Add to dashboard Cite

Image denoising is an important image processing task, both as a process itself, and as a component in other processes. The main properties of a good image denoising model are that it will remove noise while preserving edges. Traditionally, linear models have been used. One common approach is to use a Gaussian filter, In spite of the great success of many denoising algorithms; they tend to smooth the fine scale image textures when removing noise, degrading the image visual quality. To address this problem we compare two methods in this paper. The Nonlocal Hierarchical Dictionary Learning using Wavelet (NHDLW) and Gradient Histogram Preservation (GHP),which is large success in denoising. Experimental result shows that the NHDLW get significantly better denoising results especially on an image denoising algorithms on higher noise levels.

show abstract

“…As suggested in Ophir et al work [1].The wavelet based dictionary learning can further utilize the sparsity between the wavelet coefficients: …”

Section: Methodology 21 Nonlocal Hierarchical Dictionarymentioning

confidence: 99%

Section: Methodology 21 Nonlocal Hierarchical Dictionarymentioning

confidence: 99%

Nonlocal Hierarchical Dictionary Learning using Wavelets and Gradient Histogram Preservation for Image Denoising: A Review

Prajapati¹,

Gyanchandani²

2015

IJCA

View full text Add to dashboard Cite

show abstract

“…Other interesting dictionaries are characterized by several layers. Such dictionaries can be constructed as the composition of a fixed transform and learned dictionaries [20,17]. They can also be dictionaries made of two layers based on a sparsifying transform and a sampling matrix (both layers can be learnt by the algorithm investigated in [3]).…”

Section: Related Workmentioning

confidence: 99%

“…. , R}, we introduce the following indicator function 1(l,r) = 1, if (17) holds for the rth result obtained from the lth input, 0, otherwise.…”

Section: Evaluation Of P (Not Global)mentioning

confidence: 99%

Toward Fast Transform Learning

Chabiron

Malgouyres²,

Tourneret³

et al. 2014

Int J Comput Vis

View full text Add to dashboard Cite

The dictionary learning problem aims at finding a dictionary of atoms that best represents an image according to a given objective. The most usual objective consists of representing an image or a class of images sparsely. Most algorithms performing dictionary learning iteratively estimate the dictionary and a sparse representation of images using this dictionary. Dictionary learning has led to many state of the art algorithms in image processing. However, its numerical complexity restricts its use to atoms with a small support since the computations using the constructed dictionaries require too much resources to be deployed for large scale applications.In order to alleviate these issues, this paper introduces a new strategy to learn dictionaries composed of atoms obtained as a composition of K convolutions with S-sparse kernels. The dictionary update step associated with this strategy is a non-convex optimization problem. We reformulate the problem in order to reduce the number of its irrelevant stationary points and introduce a Gauss-Seidel type algorithm, referred to as Alternative Least Square Algorithm, for its resolution. The search space of the considered optimization problem is of dimension KS, which is typically smaller than the size of the target atom and is much smaller than the size of the image. The complexity of the algorithm is linear with regard to the size of the image.Our experiments show that we are able to approximate with a very high accuracy many atoms such as modified DCT, curvelets, sinc functions or cosines when K is large (say K = 10). We also argue empirically that, maybe surprisingly, the algorithm generally converges to a global minimum for large values of K and S.

show abstract

“…We propose to merge the K-SVD denoising algorithm [8] with a wavelet analysis, in a similar way to the approach taken in [12]. This will lead to an effective sparse decomposition of the image content using different scale atoms in a natural way.…”

Section: Introductionmentioning

confidence: 99%

Image denoising through multi-scale learnt dictionaries

Sulam

Ophir

Elad

2014

2014 IEEE International Conference on Image Processing (ICIP)

Self Cite

View full text Add to dashboard Cite

Over the last decade, a number of algorithms have shown promising results in removing additive white Gaussian noise from natural images, and though different, they all share in common a patch based strategy by locally denoising overlapping patches. While this lowers the complexity of the problem, it also causes noticeable artifacts when dealing with large smooth areas. In this paper we present a patch-based denoising algorithm relying on a sparsity-inspired model (K-SVD), which uses a multi-scale analysis framework. This allows us to overcome some of the disadvantages of the popular algorithms. We look for a sparse representation under an already sparsifying wavelet transform by adaptively training a dictionary on the different decomposition bands of the noisy image itself, leading to a multi-scale version of the K-SVD algorithm. We then combine the single scale and multi-scale approaches by merging both outputs by weighted joint sparse coding of the images. Our experiments on natural images indicate that our method is competitive with state of the art algorithms in terms of PSNR while giving superior results with respect to visual quality.

show abstract

Multi-Scale Dictionary Learning Using Wavelets

Cited by 148 publications

References 29 publications

Nonlocal Hierarchical Dictionary Learning using Wavelets and Gradient Histogram Preservation for Image Denoising: A Review

Nonlocal Hierarchical Dictionary Learning using Wavelets and Gradient Histogram Preservation for Image Denoising: A Review

Toward Fast Transform Learning

Image denoising through multi-scale learnt dictionaries

Contact Info

Product

Resources

About