CN109727214A - Cromogram and depth map Enhancement Method based on orthogonal sparse dictionary and grouping sparsity model - Google Patents

Abstract

The present invention discloses a kind of cromogram and depth map Enhancement Method based on orthogonal sparse dictionary and grouping sparsity model, and the orthogonal sparse dictionary building method of data-driven is expanded to multichannel image；Discrete Orthogonal sparse dictionary is constructed for each channel, and assumes that their sparse coefficient has joint sparse；The orthogonal sparse dictionary structural scheme of multi-channel data driving is applied to the joint reconstruction and enhancing of color image and depth image.

Description

Cromogram and depth map based on orthogonal sparse dictionary and grouping sparsity model enhance Method

Technical field

The invention belongs to field of image processing more particularly to a kind of coloured silks based on orthogonal sparse dictionary Yu grouping sparsity model Chromatic graph and depth map Enhancement Method.

Background technique

Image restoration is one of most important field in imaging science.Its main task is in imaging, acquisition and communication In the process, it is estimated from corrosion/noise image without the original image made an uproar, common image recovery method is based on sparsity Regularization method, it is assumed that bottom layer image has good sparse bayesian learning under certain appropriately designed systems.In fact, in the past Decades in, sparse bayesian learning not only has become the powerful of image restoration, but also in many field of signal processing, such as presses Important role is also play in contracting and data analysis.Tight wavelet frames system has proved to be sparse bayesian learning piecewise smooth image Effective system.Therefore, it is widely used in many actual image restoration problems.However, coming from different fields The image of scape is diversity so, and stationary wavelet tight frame system ideally can not sparsely approach all these scenes. Appl Comput Harmon Anal (37:89-105,2014) proposes a kind of data-driven for being adapted to specific input picture Tight frame, to realize preferably sparse approximation.The data-driven tight frame has been applied successfully to image denoising and CT image It rebuilds.

It is that there is major class image the system under good sparse bayesian learning to design that image, which restores sparse approximate basis, and there are many this The system of sample is available.Some of them are using the base of Line independent atomic building, this coefficient dimension is minimized.Sparse bayesian learning A kind of representational base is Orthogonal Wavelets such as Daubechies, I.:Ten Lectures on Wavelets, vol.61 of CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia (1992) and Mallat, S.:A wavelet tour of signal processing, Elsevier/Academic Press,Amsterdam,3rd edn.The Sparse way, With contributions from Gabriel Peyr é (2009), it only uses a small amount of non-zero small echo Coefficient can easily approach piecewise smooth image.The immense success which results in orthogonal wavelets in image procossing.So And the linear independence of base limits the quantity of atom in basic system.Therefore, the sparse bayesian learning ability based on base is limited 's.For these reasons, it is more next to sacrifice application of the excessively complete system of linear independent of the atom in base in sparse approximation It is more extensive.When while keeping Parseval identity abandon Orthogonal Wavelets in linear independent when, will obtain by Extension Principle Daubechies, I., Han, B., Ron, A., Shen, Z.:Framelets:MRA-based Constructions of wavelet frames. Appl.Comput.Harmon.Anal.14,1-46 (2003) and Ron, A.,Shen, Z.:ne systems in L2(Rd):the analysis of the analysis operator. Excessively complete Tight wavelet frames system derived from J.Funct.Anal.148,408-447 (1997).Tight wavelet frames inherit just Many advantageous properties of wavelet basis, such as efficient decomposition and restructing algorithm are handed over, but for piecewise smooth image, it compares orthogonal wavelet Base has stronger sparse bayesian learning ability.The image that Tight wavelet frames are now widely used for various tasks restores；For example, Cai, J.-F.,Chan,R.H.,Shen,L.,Shen,Z.:Convergence analysis of tight framelet Approach for missing data recovery.Adv.Comput. Math.31,87-113 (2009) and Cai, J.- F.,Dong,B.,Osher,S.,Shen, Z.:Image restoration:total variation,wavelet Frames, and beyond.J. Amer.Math.Soc.25,1033-1089 (2012), Cai, J.-F., Osher, S., Shen,Z.:Linearized Bregman iterations for frame-based image deblurring.SIAM J.Imaging Sci.2,226–252(2009).It is X-let that some other pair of image, which has fine sparse approximate excessively complete system, There are Candes, E.J., Donoho, D.L.:New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities.Comm.Pure Appl.Math.57, 219–266(2004),Labate,D.,Lim,W.-Q.,Kutyniok,G.,Weiss, G.:Sparse multidimensional representation using shearlets,In: Optics&Photonics 2005, International Society for Optics and Photonics,pp.59140U–59140U,San Diego, (2005)。

Image from true application program is varied.Different applications provide the image with different characteristic.For example, The image generated by medical imaging includes relatively little of structure for the image that digital camera generates.Even identical Under, performance of the image in different instances but differs widely.The facial image and streetscape shot with digital camera is completely not Together.Therefore, for practical problem, sparse approximation system tends not to execute well.It is known, for example, that orthogonal wavelet and Tight wavelet frames cannot all handle the image with constraint texture structure well.Based on this, Cai, J.-F., Ji, H., Shen, Z.,Ye,G.-B.:Data-driven tight frame construction and image denoising.Appl.Co Mput.Harmon.Anal.37,89-105 (2014) is recently proposed a kind of from the derived discrete tight frame of input picture itself System, the referred to as tight frame of data-driven, to be supplied to input picture.By loosening the tenth of the twelve Earthly Branches extension Principle Han, B., Kutyniok, G.,Shen,Z.:Adaptive multiresolution analysis structures and shearlet systems.SIAM J.Numer.Anal.49, 1921–1946(2011),Ron,A.,Shen,Z.:Affine systems in L2(Rd): the analysis of the analysis operator.J.Funct.Anal.148,408–447 (1997).The filtering in data-driven tight frame is obtained using the optimization that 0 norm and unitary matrice constrain, and uses alternating minimization Scheme optimizes.In order to overcome the problems, such as this, Bao, C., Ji, H., Shen, Z.:Convergence analysis for iterative data-driven tight frame construction scheme, Appl.Comput.Harmon.Anal. (2014) doi:10.1016/j.acha.2014.06.007 proposes data-driven The non-geometric convergence algorithm of tight frame construction, it was demonstrated that data drive tightly dynamic frame in image denoising Cai, J.-F., Ji, H., Shen,Z.,Ye,G.-B.:Data-driven tight frame construction and image denoising.Ap Pl.Comput.Harmon.Anal.37,89-105 (2014), image mending Bao, C., Cai, J.-F., andJi, H.: Fastsparsity-based orthogonal dictionary learning for image restoration,In: IEEE International Conference on Computer Vision,pp.3384–3391,Sydney,(2013)、 CT image reconstruction Zhou, W., Cai, J.-F., Gao, H.:Adaptive tight frame based medical image reconstruction:a proofof-concept study for computed tomography.Inverse Prob. (2013) .doi:10.1088/0266-5611/29/12/ 125006 and seismic data restore Liang, J., Ma, J., Zhang, X.:Seismic data restoration via data-driven tight frame.Geophysics 79,V65–V74 (2014) superiority in terms of.In Bao, C., Cai, J.-F., andJi, H.:Fastsparsity-based orthogonal dictionary learning for image restoration,In:IEEE International Conference on Computer Vision, pp.3384-3391, Sydney, in (2013), by the tight frame building method of data-driven again table The orthogonal dictionary learning being shown as in image block space.

Relevant knowledge

(1) Tight wavelet frames and its construction

If H is Hilbert space,It is countably infinite set.Then, we are by { x_nIt is known as the tight frame of H, if

It is found that any orthogonal basis is all tight frame.However, tight frame is not necessarily orthogonal basis.For example, two it is different just Hand over base divided byAnd be a tight frame, but be not orthogonal basis.Therefore, tight frame is the popularization of orthogonal basis.Tight frame is being protected While holding the orthogonal basis identity of Parseval, linear independence is abandoned, completeness was provided with.

Tight wavelet frames are widely used a kind of tight frames for being used for sparse bayesian learning during image restores.We fromSingle argument situation start.In Tight wavelet frames system, all functions are all the displacements of certain generators And expansion.Particularly, ifIt is one group of generator.If following system X (Ψ) exists Middle formation tight frame, then referred to as Tight wavelet frames:

The construction of Tight wavelet frames is exactly the construction of Ψ.It is a kind of former using multiresolution analysis (MRA) and tenth of the twelve Earthly Branches extension Manage the structural scheme of (UEP).We can be reconstruction φ (commonly referred to as scaling function), with one since compact support The mask α of a redesign₀Meet

Wherein,It is the Fourier transformation of φ, a₀It is one using 2 Π as the trigonometric polynomial in period, is defined asAnd meetThen it is defined in Fourier with following formulaa₀It is one using 2 Π as the trigonometric polynomial in period,X (Ψ) can form a Compact Framework when meeting the following conditions known to UEP principle:

Wherein, δ₀=1, δ₁Element in=0, ψ is referred to as frame.Sequence a₀For low-pass filtering.α₁,…,α_m-1It is high pass filter Wave.

One kind Tight wavelet frames as derived from MRA and UEP are B- spline wavelets tight frame systems.Fig. 1 describes segmented line Scaling function and frame and relevant low pass and high-pass filtering in property B- spline wavelets tight frame.

Tight wavelet frames can be obtained by tensor product:Tight wavelet frames scaling function, frame Frame and filtering be themIn corresponding tensor product.

Digital picture isIn vector, beThe discretization of middle function.Using with appropriate boundary condition Tight wavelet frames transformation, can construct the tight frame system of digital picture.The structure is converted by discrete wavelet tight frame and is exported.IfIt is low pass associated with Tight wavelet frames and high-pass filter.If a × b is two vectorsFiltering become It changes, is considered as having the two-dimensional array of N × N size of appropriate boundary condition.Then, one layer of translation invariant discrete wavelet tight frame Transformation is linear transformation.

Tenth of the twelve Earthly Branches condition (2.1) and UEP (2.2) mean W^TW=I.In other words, the row of W existsOne tight frame of middle formation Frame.

(2) construction of data-driven tight frame

Since Tight wavelet frames are determined by the filtering of Tight wavelet frames completely, the construction of data-driven tight frame is logical It crosses and the filtering of Tight wavelet frames is constructed to realize.Regardless of what bottom layer image is, the tight frame of data-driven is not Using Static Filtering, but use the filtering customized according to specific input picture.Particularly, it enablesIt is 2 dimensions filtering race, under Wen Zhong, we will not distinguishThe set of filtering and the matrix for filtering H.By (2.3), associated tight frame transformation is

Wherein * is the filtering transformation of two 2 dimension arrays.In order to makeRow existIt is middle to form one Tight frame, it should meet W (H)^ΤW (H)=I reconstruction nature.Using UEP, we obtain following theorem.

Theorem 2.1: assuming thatR is integer, and H is classified as the 2D array that size is r × r Vectorization.Therefore, if H^ΤThe column of H=I/R, W (H) constitute a tight frame.

It enablesAs input picture, a tight frame in order to obtain, in the rest part of this section, we be will assumeR=r², r is integer, and H is classified as the vectorization that size is the 2D array of r × r.In the help of theorem 2.1 Under, the tight frame structure type of data-driven can be turned into following minimization problem

Wherein, | | v | |₀It is the 0- norm of v, the first item of cost function is to make coefficient in (2.5)Close to W (H) G, Section 2 are to reinforce the sparsity of v.According to theorem 2.1, constraint can guarantee that W (H) is a tight frame.Therefore, pass through (2.5) we have obtained one group of filtering H and a tight frame W (H), and input picture has sparse coefficient under the frame.With friendship For direction minimization scheme numerical solution equation (2.5).

1) H is determined, minimization problem (2.5) becomes:Its solution is (2.6)

V=T_λ(W(H)g)

Be hard limiting operator definitions be T_λ(x)=x χ_|x|>=λ, χ_|x|>=λ is | x | the feature vector of >=λ.

2) determine that vector v, minimization problem (2.5) become:

The closed solutions of (2.7) are provided with singular value decomposition (SVD), and are summarised in following theorem.

Theorem 2.2: assuming thatIt is one g is sampled to obtain the matrix of r × r image block composition, regards one as The matrix of a N × N.It enablesIt is to be rearranged to v, is risen in this way, the jth column of V are corresponding with the coefficient of j-th of pixel Come.Enable GV^Τ=P ∑ Q^ΤAs GV^Τ(2.8)

Singular value decomposition, then 2.7 solution is as follows: H=PQ^Τ/r

Finally, the construction of the tight frame g of data-driven is alternate application formula (2.6) and (2.8).

Summary of the invention

Technology of the invention solves the problems, such as: overcoming deficiency existing for existing orthogonal sparse dictionary, provides a kind of based on just Hand over the cromogram and depth map Enhancement Method of sparse dictionary and grouping sparsity model

To achieve the above object, the present invention adopts the following technical scheme that:

A kind of cromogram based on orthogonal sparse dictionary and grouping sparsity model includes following step with depth map Enhancement Method It is rapid:

Step 1: being separately added into noise in colored RGB channel and depth channel；

Step 2: initialization multichannel imageI.e. RGB channel and depth channel are initialised to togetherIn, initially Change filtering collection The orthogonal sparse dictionary in corresponding i-th of channel；

Step 3: enablingWhereinη⁽ⁱ⁾For noise, Λ is the position that pixel is observed in depth image Set, P_ΛIt is diagonal matrix, wherein the element on diagonal line is 0 or 1, is if depositing in the position in observation position set Λ 1, it is otherwise 0,It is on set Λ to image g⁽⁴⁾Reconstruction；

Step 4: constructing a multi-channel data using the building method (algorithm one) of multi-channel data driving Compact Framework Driver framework

Step 5: by thresholding multi-channel quadrature sparse dictionary coefficient to image

G_(k-1/2)Denoising

W(H⁽ⁱ⁾) be consistent orthogonal sparse dictionary transformation, v⁽ⁱ⁾For g under the transformation⁽ⁱ⁾Coefficient, T_λ,ω,rowBe row to Hard -threshold operator is measured, formula the first row is to multi-channel quadrature sparse dictionary coefficient v⁽ⁱ⁾Thresholding, the second row is to pass through threshold Coefficient and orthogonal sparse dictionary operation after value achieve the effect that denoise each channel of image.

Step 6: exiting circulation if meeting stop condition；Otherwise, return step three；

Output: the coloured picture g of denoising⁽ⁱ⁾, i=1,2,3 and rebuild after depth map g⁽⁴⁾。

Detailed description of the invention

Scaling function and frame in Fig. 1 piecewise linearity B-spline Tight wavelet frames；

Fig. 2 and LRMC method for reconstructing PSNR Comparative result；

Fig. 3 and LRMC method for reconstructing visual effect compare.

Specific embodiment

The present invention provides a kind of cromogram and depth map Enhancement Method based on orthogonal sparse dictionary and grouping sparsity model, The orthogonal sparse dictionary building method of data-driven is expanded into multichannel image.We construct Discrete Orthogonal for each channel Sparse dictionary, and assume that their sparse coefficient has joint sparse.The orthogonal sparse dictionary structure that multi-channel data is driven Scheme is made to rebuild and enhance applied to the joint of color image and depth image.

Problem description:

We construct a Discrete Orthogonal sparse dictionary for each channel of color image and depth image, and assume it Sparse coefficient have common sparse mode.This cause one constrained comprising 0 norm of vector and several orthogonal matrixes it is excellent Change problem.Details is as follows:

Enable G=[g⁽¹⁾,g⁽²⁾,…,g^(c)] it is a multichannel image, whereinIndicate i-th of channel, because Each channel includes different characteristic information, we are respectively each channel building orthogonal sparse dictionary.Enable H⁽ⁱ⁾, i=1 ..., c As the orthogonal sparse dictionary in i-th of channel, and W (H⁽ⁱ⁾), it is converted as their consistent orthogonal sparse dictionaries, such as formula It is explained in 2.4.We assume that for arbitraryR is integer, and H⁽ⁱ⁾Be classified as Size is 2 dimension groups of the vector form of r × r.In W (H⁽ⁱ⁾) under transformation, g⁽ⁱ⁾Coefficient indicated with v (i), and write as V=[v⁽¹⁾,v⁽²⁾,…,v^(c)].Since the channel in image G is all interaction, the sparsity of the column of V should mutually be closed Connection.We assume that the column of V have common sparse mode, it is assumed that most several rows in V are null vectors.It is this in order to promote Joint sparse, we use | | V | |_0,rowAs regularization term, as follows

Wherein, v_jIt is j-th of column of V, andIt is v_j≠ 0 characterization function.Function | | | |_0,rowIt is zero model Count to the popularization of vector Value Data.

By solving following minimization problem, we construct the orthogonal sparse dictionary of data-driven for multichannel image.

s.t.(H⁽¹⁾)^TH⁽¹⁾=...=(H^(c))^TH^(c)=I/R

Wherein ω_i, it is normal number that i=1 ..., c, which represent different channels,.First item in objective function 3.1 is that data are protected True item guarantees g⁽ⁱ⁾Coefficient v⁽ⁱ⁾In Discrete Orthogonal sparse dictionary variation W (H⁽ⁱ⁾) under；Section 2 is regular terms, so that V Meet sparse prior.Constraint condition and to H⁽ⁱ⁾Additive postulate, guarantee W (H⁽ⁱ⁾), i=1 ..., c is an orthogonal sparse word The transformation of allusion quotation.

In color image, due to considering channel relevancy significantly in the construction of multi-channel quadrature sparse dictionary. The mathematical description that and depth image colored to joint is rebuild is as follows.If g⁽¹⁾、g⁽²⁾And g⁽³⁾It is the red of color image respectively (R), green (G) and blue channel (B), g⁽⁴⁾It is the channel depth (D).Observed image (make an uproar color image and imperfect depth of making an uproar Degree image) include:

Wherein, η⁽ⁱ⁾, i=1,2,3,4 be noise, and Λ is the position collection that pixel is observed in depth image, x_ΛIt is the pact of x Beam.Want to rebuild RGB channel and D channel, RGB-D channel image Problems of Reconstruction can be regarded as only with the missing picture in the channel D The problem of element is repaired.Assuming that we, which have constructed one, has filtering H⁽ⁱ⁾, i=1 ..., the multi-channel quadrature of c is sparse Dictionary.By the inspiration of orthogonal sparse dictionary patch algorithm, multi-channel quadrature sparse dictionary patch algorithm is

Wherein P_ΛDiagonal matrix, diagonal element is made of 0 and 1, if position in set Λ, value be 1, otherwise for 0.Enable g⁽⁴⁾As the prediction of D channel, we replace with its pixel by observingIn Λ.The estimation of D channelObserved image band is combined to make an uproar RGB channel f⁽ⁱ⁾, i=1,2,3, the step 2 that can be applied in (4.1) and 3 denoising Mechanism.

The technical solution of the invention is as follows: orthogonal sparse to being driven based on multi-channel data using the method for alternative optimization The sparse Optimized model of dictionary solves.The following steps are included:

Step 1: fixed H⁽ⁱ⁾, i=1 ..., c or coefficient V, (3.1) are solved only with respect to its dependent variable.As filtering H⁽¹⁾,…,H^(c)When fixed, the solution (3.1) about V can be expressed as again

About the closing form of (3.2) solution, we have following theorem.

Theorem 3.1:(3.2) solution be V=T_λ,ω,row([W(H⁽¹⁾)g⁽¹⁾,...,W(H^(c))g^(c)]) (3.3) Wherein T_λ,ω,rowIt is row vector hard -threshold operator, just like giving a definition: X and T_λ,ω,rowJth row be expressed as [T_λ,ω,row (X)]_jAnd x_j, then

WhereinIt is 2 norms of a weighting.

It proves: enabling X=[W (H⁽¹⁾g⁽¹⁾),…,W(H^(c)g^(c))] enable x_ijAnd x_jRespectively represent i-th, the j entrance and jth of X Row, then can be re-written as:Wherein j=1 ..., N²Mean that (3.2) are separated into N² A independent small-scale minimization problem.If solution (3.4) is v_j.If x_j=0, it is evident that the solution of (3.4) is v_j=0. Therefore we assume that x_j=0. by considering v respectively_j≠ 0 and v_j=0 the case where, (3.4) are rearranged for by we

Obviously, the minimum value in the case of the first is v_j=x_j≠ 0, associated minimum value is λ².Therefore, if | | x_j||_ω >=λ, then by selecting the first situation to obtain minimum value, and minimum value is v_j=x_j, otherwise pass through selection second situation Minimum value is obtained, and minimum value is v_j=0.

Step 2: when coefficient V is to determine.Solve H⁽ⁱ⁾, i=1 ..., c are equivalent to solve following c unrelated minimums Change problem

According to theorem 2.2, the solution of (3.5) has closing form: H⁽ⁱ⁾=P⁽ⁱ⁾(Q⁽ⁱ⁾)^T/r (3.6) P⁽ⁱ⁾,Q⁽ⁱ⁾It is G⁽ⁱ⁾ (V⁽ⁱ⁾)^Τ=P⁽ⁱ⁾(Q⁽ⁱ⁾)^ΤThe singular matrix of singular value decomposition.It is by g⁽ⁱ⁾R × r sampling block composition square Battle array, is considered as N × N number of 2D matrix.

It is to v⁽ⁱ⁾Reconstruct, such v⁽ⁱ⁾Jth column can be mapped with the coefficient of pixel j.

One multi-channel data of algorithm drives the building input of orthogonal sparse dictionary: the image G=[g containing c channel⁽¹⁾,...,g^(c)], the filtering collection A of initialization⁽ⁱ⁾, i=1 ..., c output: the orthogonal sparse dictionary H of multi-channel data driving⁽ⁱ⁾, i=1 ..., c

Initialization: by the way that A is arranged⁽ⁱ⁾, i=1 ..., c initializes H⁽ⁱ⁾, i=1 ..., c；

Into outer loop k=1,2 ..., K

1) by (3.3) andUpdate coefficient V；

2) enter interior loop, update

A) matrix G is constructed⁽ⁱ⁾And V⁽ⁱ⁾

B) singular value is calculated

C) it is obtained by (3.6) formula

Interior loop terminates

If 3) meet condition, K=k is enabled, terminates outer loop；

4) it exportsEmbodiment 1:

Step 1: standard deviation=25 and the white Gaussian noise of d=5 are separately added into RGB channel and depth channel, it is color Color noisy image f⁽ⁱ⁾, i=1,2,3；Band is made an uproar incomplete depth imageΛ is the pixel set in known depth map.

Step 2: initialization.Initialization filtering collectionFor the dct transform of 8*8 size；RGB channel is set W1=w2=w3=1；According to the ratio between 2 norms of initial color image and initial depth image, select the range of w4 for [1, 5]。

Step 3: acquisition color channel information and depth channel information, to initialize

Step 4: enabling image

Step 5: constructing one using the building method of channel data driving Compact Framework

Multi-channel data driver framework

Step 6: by thresholding multi-channel quadrature sparse dictionary coefficient to image G_(k-1/2)Denoising:

Step 7: exiting circulation if meeting stop condition；Otherwise, return step four.

Output: the coloured picture g of denoising⁽ⁱ⁾, i=1,2,3 and rebuild after depth map g⁽⁴⁾

The invention proposes a kind of cromogram based on orthogonal sparse dictionary and grouping sparsity model and depth map enhancing sides Method, which, which is applied to colored and depth joint image (RGB-D image), enhances.Experiment shows this method ratio Existing joint is colored and depth image method for reconstructing has better performance, as shown in Figure 2,3.

Claims (1)

1. a kind of cromogram and depth map Enhancement Method based on orthogonal sparse dictionary and grouping sparsity model is it is characterized in that, packet Containing following steps:

Step 1: being separately added into noise in colored RGB channel and depth channel；

Step 2: initialization multichannel imageI.e. RGB channel and depth channel are initialised to togetherIn, initialization filtering Collection The orthogonal sparse dictionary in corresponding i-th of channel；

Step 3: enablingWherein f⁽ⁱ⁾=g⁽ⁱ⁾+η⁽ⁱ⁾, i=1,2,3,η⁽ⁱ⁾For noise, Λ is the location sets that pixel is observed in depth image, P_ΛIt is diagonal matrix, wherein right Element on linea angulata is 0 or 1, is 1 if depositing in observation position set Λ in the position, is otherwise 0,It is on Λ to g⁽⁴⁾Reconstruction；

It is driven Step 4: constructing a multi-channel data using the building method (algorithm one) of multi-channel data driving Compact Framework Frame

Step 5: by thresholding multi-channel quadrature sparse dictionary coefficient to image G_(k-1/2)Denoising

W(H⁽ⁱ⁾) be consistent orthogonal sparse dictionary transformation, v⁽ⁱ⁾For g under the transformation⁽ⁱ⁾Coefficient, T_λ,ω,rowIt is that row vector is hard Threshold operator, formula the first row are to multi-channel quadrature sparse dictionary coefficient v⁽ⁱ⁾Thresholding, the second row is to pass through thresholding The operation of coefficient and corresponding transformed Compact Framework afterwards achievees the effect that denoise each channel of image.

Step 6: exiting circulation if meeting stop condition；Otherwise, return step three；

Output: the coloured picture g of denoising⁽ⁱ⁾, i=1,2,3 and rebuild after depth map g⁽⁴⁾。