Patch-based models and algorithms for image denoising: a comparative review between patch-based images denoising methods for additive noise reduction

Abstract

Background: Digital images are captured using sensors during the data acquisition phase, where they are often contaminated by noise (an undesired random signal). Such noise can also be produced during transmission or by poor-quality lossy image compression. Reducing the noise and enhancing the images are considered the central process to all other digital image processing tasks. The improvement in the performance of image denoising methods would contribute greatly on the results of other image processing techniques. Patch-based denoising methods recently have merged as the state-of-the-art denoising approaches for various additive noise levels. In this work, the use of the state-of-the-art patch-based denoising methods for additive noise reduction is investigated. Various types of image datasets are addressed to conduct this study.

Methods: We first explain the type of noise in digital images and discuss various image denoising approaches, with a focus on patch-based denoising methods. Then, we experimentally evaluate both quantitatively and qualitatively the patch-based denoising methods. The patch-based image denoising methods are analyzed in terms of quality and computational time.

Results: Despite the sophistication of patch-based image denoising approaches, most patch-based image denoising methods outperform the rest. Fast patch similarity measurements produce fast patch-based image denoising methods.

Conclusion: Patch-based image denoising approaches can effectively reduce noise and enhance images. Patch-based image denoising approach is the state-of-the-art image denoising approach.

Keywords: BM3D; Bilateral filter; Dictionary learning filtering; Gaussian patch-PCA filtering; K-SVD; Non-local means filtering; Patch-based image denoising; Probabilistic patch-based filtering.

Fig. 1

Image denoising approaches: a filtering based on neighboring pixels located within a kernel in pixel-based denoising schemes and b filtering based on patches located within a search window in patch-based denoising schemes

Fig. 2

Similarity between patches. a NL-Means patches as a raster scan in a search window. b Patch P3 is similar to P1 more than patch P2; hence, P3 will get a weight larger than P2 weight

Fig. 3

Weights in PPB algorithm: computing iteratively the weights between two pixels s and t in the probabilistic patch-based (PPB) filter. The PPB weights estimator (PPBWE) uses the noisy image and the estimation values from the previous iteration in order to estimate the weight

Fig. 4

K-SVD filter: dictionary learning scheme of the K-SVD filter

Fig. 5

Patches of PB-PCA method: extracting patches in PB-PCA method and grouping them before PCA

Fig. 6

The principal components “axis” of the house image: a is the input image, b is the first 16 principal axes of the all patches obtained from the house image, and c is the last 16 principal axes of the all patches obtained from the house image [13]

Fig. 7

Different PB-PCA projections: a comparison between PSNR of the different methods of the projections in PB-PCA for the House and Cameraman images. The threshold ratio (λ/σ) into the bottom of x-axis controls the number of axes kept in the upper x-axis. σ is the noise variation, and λ is chosen by cross validation [13]

Fig. 8

Collecting a set of patches in PB-PCA filtering: a global PCA, b local PCA, and c hierarchical PCA

Fig. 9

BM3D filtering: the two steps of BM3D filtering [11]

Fig. 10

The four used images in the experiment: a Barbara image 512×512, b House image 256×256, c CurvedBand image 257×257, and d Chessboard image 256×256

Fig. 11

Denoising methods performance: the performance of the denoising methods for the four images at various noise levels (σ)

Fig. 12

The performance charts: four charts summarize the performance of the denoising methods for the four images when the noise is low (σ=10)

Fig. 13

The performance charts: four charts summarize the performance of the denoising methods for the four images when the noise is low (σ=20)

Fig. 14

The efficiency charts: four charts show the average of the consumed time in seconds for various denoising methods excluding K-SVD

Fig. 15

Denoised Barbara images: a Original Barbara image; b AWG noise, σ=40; c AD ; d bilateral filtering, e NL-Means filtering, f K-SVD, g BM3D, h non-itPPB, i it-PPB, j PGPCA, k PLPCA, and l PHPCA

Fig. 16

Zoomed images of the denoised Barbara image shown in Fig. 15: a original Barbara’s pant; b AWG noise, σ=40; c AD (Perona & Malik); d bilateral filtering; e NL-Means filtering; f K-SVD; g BM3D; h Non-itPPB; i It-PPB; j PGPCA; k PLPCA; and l PHPCA

Fig. 17

Zoomed images of the denoised Barbara image shown in Fig. 15: a original Barbara’s eye cover fold; b AWG noise, σ=40; c AD (Perona & Malik); d bilateral filtering; e NL-Means filtering; f K-SVD; g BM3D; h Non-itPPB; i It-PPB; j PGPCA; k PLPCA; and l PHPCA

Fig. 18

Denoised House images: a original House image; b AWG noise, σ=40; c AD (Perona & Malik); d bilateral filtering; e NL-Means filtering; f K-SVD; g BM3D; h Non-itPPB; i It-PPB; j PGPCA; k PLPCA; and l PHPCA

Fig. 19

Denoised CurvedBand images: a original CurvedBand image; b AWG noise, σ=40; c AD (Perona & Malik); d bilateral filtering; e NL-Means filtering; f K-SVD; g BM3D; h Non-itPPB; i It-PPB; j PGPCA; k PLPCA; and l PHPCA

Fig. 20

Zoomed images of the denoised CurvedBand image shown in Fig. 19: a original CurvedBand image; b AWG noise, σ=40c AD (Perona & Malik); d bilateral filtering; e NL-Means filtering; f K-SVD; g BM3D; h Non-itPPB; i It-PPB; j PGPCA; k PLPCA; and l PHPCA

Fig. 21

Denoised Chessboard images: a original Chessboard image; b AWG noise, σ=40; c AD (Perona & Malik); d bilateral filtering; e NL-Means filtering; f K-SVD; g BM3D; h Non-itPPB; i It-PPB; j PGPCA; k PLPCA; and l PHPCA