MDL Denoising Revisited

We refine and extend an earlier MDL denoising criterion for wavelet-based denoising. We start by showing that the denoising problem can be reformulated as a clustering problem, where the goal is to obtain separate clusters for informative and non-informative wavelet coefficients, respectively. This suggests two refinements, adding a code-length for the model index, and extending the model in order to account for subband-dependent coefficient distributions. A third refinement is derivation of soft thresholding inspired by predictive universal coding with weighted mixtures. We propose a practical method incorporating all three refinements, which is shown to achieve good performance and robustness in denoising both artificial and natural signals.Comment: Submitted to IEEE Transactions on Information Theory, June 200

Bayesian demosaicing using Gaussian scale mixture priors with local adaptivity in the dual tree complex wavelet packet transform domain

In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. ABSTRACT In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU

Wavelet Domain Image Separation

In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution of the wavelet coefficients of real world images can naturally be modeled by an exponential power probability density function. The Bayesian approach which has been used with success in blind source separation gives also the possibility of including any prior information we may have on the mixing matrix elements as well as on the hyperparameters (parameters of the prior laws of the noise and the sources). We consider two cases: first the case where the wavelet coefficients are assumed to be i.i.d. and second the case where we model the correlation between the coefficients of two adjacent scales by a first order Markov chain. This paper only reports on the first case, the second case results will be reported in a near future. The estimation computations are done via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the performances of the proposed method. Keywords: Blind source separation, wavelets, Bayesian estimation, MCMC Hasting-Metropolis algorithm.Comment: Presented at MaxEnt2002, the 22nd International Workshop on Bayesian and Maximum Entropy methods (Aug. 3-9, 2002, Moscow, Idaho, USA). To appear in Proceedings of American Institute of Physic

Kajian motivasi ekstrinsik di antara Pelajar Lepasan Sijil dan Diploma Politeknik Jabatan Kejuruteraan Awam KUiTTHO

Kajian ini dijalankan untuk menyelidiki pengaruh dorongan keluarga, cara pengajaran pensyarah, pengaruh rakan sebaya dan kemudahan infrastruktur terhadap motivasi ekstrinsik bagi pelajar tahun tiga dan tahun empat lepasan sijil dan diploma politeknik Jabatan Kejuruteraan Awain Kolej Universiti Teknologi Tun Hussein Onn. Sampel kajian ini beijumlah 87 orang bagi pelajar lepasan sijil politeknik dan 38 orang bagi lepasan diploma politeknik. Data kajian telah diperolehi melalui borang soal selidik dan telah dianalisis menggunakan perisian SPSS (Statical Package For Sciences). Hasil kajian telah dipersembahkan dalam bentuk jadual dan histohgrapi. Analisis kajian mendapati bahawa kedua-dua kumpulan setuju bahawa faktor-faktor di atas memberi kesan kepada motivasi ekstrinsik mereka. Dengan kata lain faktpr-faktor tersebut penting dalam membentuk pelajar mencapai kecemerlangan akademik

Implementasi Image Denoising dengan Menggunakan Gaussian Scale Mixtures pada Domain Wavelet

ABSTRAKSI: Citra digital adalah salah satu bentuk citra yang paling mudah dipergunakan dari segi pengiriman citra sebagai data, pengolahan dan pemrosesan citra itu sendiri. Seringkali dalam proses pengiriman citra, yang dikirimkan mengalami noise yang mengakibatkan kulitas citra yang dikirimkan menjadi tidak sesuai / berbeda dengan citra aslinya pada saat citra digital itu diterima karena adanya distorsi sewaktu transmisi. Dalam tugas akhir ini akan diimplementasikan dan dianalisis pemakaian metode Gaussians Scale Mixtures (GSM) pada domain wavelet dalam melakukan proses denoising. Dengan metode ini digunakan dua variabel random yang terpisah satu sama lain, yaitu Gaussian vector dan hidden positive scalar multiplier, dimana keduanya memodelkan skala dan koefisien ketetanggaan yang posisinya berdekatan. Di dalam metode GSM ini digunakan estimasi Bayes Least Square (BLS) untuk mengestimasi bobot pixel ter-noise sehingga didapatkan kembali nilai pixel tersebut yang mendekati nilai aslinya. Noise yang digunakan ialah additive gaussian noise yang akan dibangkitkan melalui suatu noise generator. Parameter performansi yang diujikan pada citra digital adalah PSNR (Peak Signal-to-Noise Ratio) dan MOS (Mean Opinion Score) pada citra hasil denoising. Pengujian dilakukan dengan beberapa kombinasi, yaitu wavelet filter (daubechies-1 s/d 4), ukuran matrik ketetanggaan BLS (3x3, 5x5, 7x7), dan standar deviasi noise 10, 30 dan 50. Dari hasil analisis didapatkan bahwa peningkatan ordo wavelet daubechies tidak mempengaruhi nilai PSNR citra hasil denoising secara significan dan semakin besar ukuran matrik BLS, maka peningkatan nilai PSNR juga semakin kecil.Kata Kunci : additive gaussian noise, Gaussian Scale Mixtures (GSM), Bayes Least Square (BLS), PSNR, MOSABSTRACT: Digital image is one of the easiest used image forms viewed from the sending of image as data and the image processing itselves. In the image sending, it often happened the sent image is contained by noise then makes image quality is different with the original image when the image is received, it because of there is a distortion during transmission. This final task would be implemented and analysed the using of Gaussians Scale Mixtures (GSM) method in the wavelet domain during denoising process. This method used two independent random variable, i.e. Gaussian vector and hidden positive scalar multiplier, in which both of them modeled scale and close neighbourhood coeffcien. In this GSM method used Bayes Least Square (BLS) estimation for estiamating the weight of noisy pixels to get back that pixel value that is the most close to its real value. Performance parameters that would be tested in the digital image are PSNR (Peak Signal-to-Noise Ratio ) and MOS (Mean Opinion Score) on result of denoising image. The testing were did with several combination, i.e. wavelet filter (daubechies-1 to daubechies-4), BLS neighbourhood matrix size (3x3, 5x5, 7x7), and noise standar deviation (10, 30 dan 50). From the result of analysist got that the increasing of daubechies wavelet ordo does not impact PSNR value of the result of denoising image significantly and as the bigger of BLS matrix size as the increase PSNR value is getting lower.Keyword: Additive Gaussian Noise, Gaussian Scale Mixtures (GSM), Bayes Least Square (BLS), PSNR, MO