On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them

Aharon, Michal; Elad, Michael; Bruckstein, Alfred M.

doi:10.1016/j.laa.2005.06.035

Cited by 171 publications

(192 citation statements)

References 28 publications

Supporting

Mentioning

188

Contrasting

Order By: Relevance

“…To do this, we can use methods such as gradient descent in a probabilistic framework [39], [40] or the recent K-SVD algorithm [41]. When applied to MIDI-synthesized harpsichord music, this simple model is able to identify most of the notes present in the piece, and produce a sparse 'pianoroll' representation of the music, a simple version of automatic music transcription (Fig.…”

Section: Automatic Music Transcriptionmentioning

confidence: 99%

Sparse Representations in Audio and Music: From Coding to Source Separation

et al. 2010

View full text Add to dashboard Cite

Abstract-Sparse representations have proved a powerful tool in the analysis and processing of audio signals and already lie at the heart of popular coding standards such as MP3 and Dolby AAC. In this paper we give an overview of a number of current and emerging applications of sparse representations in areas from audio coding, audio enhancement and music transcription to blind source separation solutions that can solve the "cocktail party problem". In each case we will show how the prior assumption that the audio signals are approximately sparse in some time-frequency representation allows us to address the associated signal processing task.

show abstract

Section: Automatic Music Transcriptionmentioning

confidence: 99%

Sparse Representations in Audio and Music: From Coding to Source Separation

et al. 2010

View full text Add to dashboard Cite

show abstract

“…The tested noise level of each input image is all the same as sparse coding method [14] used in denoising experiments, so as to guarantee a fair comparison.…”

Section: Resultsmentioning

confidence: 99%

“…Choosing a suitable dictionary is important for this framework. The concept of dictionary learning that generates sparse representation for a set of training image patches has been studied in a series of work [7][8][9][10][11][12][13][14]. In this work, the dictionary is trained by using patches from the noisy image itself.…”

Section: Image Denoising Via Improved Sparse Codingmentioning

confidence: 99%

Image Denoising via Improved Sparse Coding

Lu¹,

Yuan²,

Yan³

et al. 2011

Procedings of the British Machine Vision Conference 2011

View full text Add to dashboard Cite

This paper presents a novel dictionary learning method for image denoising, which removes zero-mean independent identically distributed additive noise from a given image. Choosing noisy image itself to train an over-complete dictionary, the dictionary trained by traditional sparse coding methods contains noise information. Through mathematical derivation of equation, we found that a lower bound of dictionary is related with the level of noise in dictionary learning. The proposed idea is to take advantage of the noise information for designing a sparse coding algorithm called improved sparse coding (ISC), which effectively suppresses the noise influence for training a dictionary. This denoising framework utilizes the effective method, which is based on sparse representations over trained dictionaries. Acquiring an over-complete dictionary by ISC mainly includes three stages. Firstly, we utilize K-means method to group the noisy image patches. Secondly, each dictionary is trained by ISC in corresponding class. Finally, an over-complete dictionary is merged by these dictionaries. Theory analysis and experimental results both demonstrate that the proposed method yields excellent performance.

show abstract

“…The result enhances the degree of compression and the accuracy of reconstruction. Sparse representation with learned transforms outperforms predefined transforms in a range of image processing applications such as de-noising, de-blurring and in-painting [36][37][38]. Furthermore, the recent work in Stevens et al [39] showed the feasibility of using the dictionary learning-based technique to infer missing pixels in STEM images from scanning a random selection of just 5% of the total number of pixels in the image area.…”

Section: Three-dimensional Image Reconstructionmentioning

confidence: 99%

Linear chemically sensitive electron tomography using DualEELS and dictionary-based compressed sensing

et al. 2016

View full text Add to dashboard Cite

I. (2016) Linear chemically sensitive electron tomography using DualEELS and dictionary-based compressed sensing. Ultramicroscopy.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.http://eprints.gla.ac.uk/122396/ A B S T R A C TWe have investigated the use of DualEELS in elementally sensitive tilt series tomography in the scanning transmission electron microscope. A procedure is implemented using deconvolution to remove the effects of multiple scattering, followed by normalisation by the zero loss peak intensity. This is performed to produce a signal that is linearly dependent on the projected density of the element in each pixel. This method is compared with one that does not include deconvolution (although normalisation by the zero loss peak intensity is still performed). Additionally, we compare the 3D reconstruction using a new compressed sensing algorithm, DLET, with the well-established SIRT algorithm. VC precipitates, which are extracted from a steel on a carbon replica, are used in this study. It is found that the use of this linear signal results in a very even density throughout the precipitates. However, when deconvolution is omitted, a slight density reduction is observed in the cores of the precipitates (a so-called cupping artefact). Additionally, it is clearly demonstrated that the 3D morphology is much better reproduced using the DLET algorithm, with very little elongation in the missing wedge direction. It is therefore concluded that reliable elementally sensitive tilt tomography using EELS requires the appropriate use of DualEELS together with a suitable reconstruction algorithm, such as the compressed sensing based reconstruction algorithm used here, to make the best use of the limited data volume and signal to noise inherent in core-loss EELS.

show abstract

On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them

Cited by 171 publications

References 28 publications

Sparse Representations in Audio and Music: From Coding to Source Separation

Sparse Representations in Audio and Music: From Coding to Source Separation

Image Denoising via Improved Sparse Coding

Linear chemically sensitive electron tomography using DualEELS and dictionary-based compressed sensing

Contact Info

Product

Resources

About